Skip to main content
SpringerLink
Log in

SCAN-98 Collected Bibliography

  • Chapter
Developments in Reliable Computing

  • 372 Accesses

Abstract

This is a bibliography of work related to interval arithmetic and validated computation. It represents the compilation of all works cited by the papers in this volume.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. P. Abbott and R. P. Brent, Fast local convergence with single and multistep methods for nonlinear equations, Austr. Math. Soc. (Series B), 19 (1997), pp. 173–199.

    Article  MathSciNet  Google Scholar 

  2. E. Adams, D. Cordes, and R. J. Lohner, Enclosure of solutions of ordinary initial value problems and applications, in Discretization in Differential Equations and Enclosures, E. Adams, R. Ansorge, C. Großmann, and H. G. Roos, eds., Akademie-Verlag, Berlin, 1987, pp. 9–28.

    Google Scholar 

  3. N. I. Ahieser, Elements of the Elliptic Functions Theory,Nauka, Moscow, 1970. In Russian.

    Google Scholar 

  4. A. Akritas, A. Bocharov, and A. Strzebonski, Implementation of real root isolation algorithms in Mathematica, in Conference Materials of Interval ‘84 (St. Petersburg, Russia, 1994 ), 1994, pp. 23–27.

    Google Scholar 

  5. G. Alefeld and J. Herzberger, Einfiihrung in die Intervallrechnung, Springer-Verlag, Heidelberg, 1974.

    Google Scholar 

  6. G. Alefeld, Introduction to Interval Computations, Academic Press, New York, 1983.

    MATH  Google Scholar 

  7. G. Alefeld and G. Meyer, The Cholesky method for interval data, Linear Algebra Appl., 194 (1993), pp. 161–182.

    Article  MathSciNet  MATH  Google Scholar 

  8. P. Alessandri and V. Bertha, Three distance theorems and combinatorics on words, Research Report, Institut de Mathématiques de Luminy, Marseille, France, 1997.

    Google Scholar 

  9. E. anderson, Z. BAI, C. Bischof, J. Demmel, J. Dongarra, J. Du Croz, A. Green-Baum, S. Hammarling, A. Mckenney, S. Ostrouchov, and D. C. Sorensen, LAPACK User’s Guide, Release 2.0, SIAM, Philadelphia, second ed., 1995.

    Google Scholar 

  10. ANSI/ISO, Working paper for draft proposed international standard for information systems programming language C++,Tech. Report ANSI X3J16/96–0225 ISO WG21/N1043, ANSI/ISO, 1996.

    Google Scholar 

  11. E. S. Armstrong, An extension of Bass’ algorithm for stabilizing linear continuous constant systems, IEEE Trans. Automat. Control, AC-20 (1975), pp. 153–154.

    Google Scholar 

  12. R. Barnhill, G. Farin, M. Jordan, and B. Piper, Surface/surface intersection, Computer Aided Geometric Design, 4 (1987), pp. 3–16.

    Article  MathSciNet  MATH  Google Scholar 

  13. W. Barth, R. Lieger, and M. Schindler, Ray tracing general parametric surfaces using interval arithmetic, The Visual Computer, 10 (1994), pp. 363–371.

    Article  Google Scholar 

  14. W. Barth and E. Nuding, Optimale Lösung von Intervallgleichungssystemen, Computing, 12 (1974), pp. 117–125.

    Article  MathSciNet  MATH  Google Scholar 

  15. H. Bauch, K. Jahn, D. Oelschlägel, H. SÜSse, and V. Wiebigke, Intervallmathematik Theorie und Anwendungen, Teubner, Leipzig, 1987.

    MATH  Google Scholar 

  16. C. Bendsten and O. Stauning, FADBAD, a flexible C++ package for automatic differentiation using the forward and backward methods, Tech. Report 1996-x5–94, Department of Mathematical Modelling, Technical University of Denmark, Lyngby, Denmark, August 1996.

    Google Scholar 

  17. C. Bendsten, Tadiff, a flexible C++ package for automatic differentiation using Taylor series, Tech. Report 1996-x5–94, Department of Mathematical Modelling, Technical University of Denmark, Lyngby, Denmark, April 1997.

    Google Scholar 

  18. F. Benhamou, F. Goualard, and L. Granvilliers, Programming with the DecLIC language, in Proceedings of the Second Workshop on Interval Constraints (October 1997, Port-Jefferson, NY ), 1997.

    Google Scholar 

  19. F. Benhamou, D. Mcallester, and P. Van Hentenryck, Clp(intervals) revisited, in Proceedings of the 1994 International Symposium, M. Bruynooghe, ed., MIT Press, 1994, pp. 124–138.

    Google Scholar 

  20. F. Benhamou and W. Older, Applying interval arithmetic to real, integer and Boolean constraints, Journal of Logic Programming, 32 (1997), pp. 1–24.

    Article  MathSciNet  MATH  Google Scholar 

  21. S. Berner, Ein paralleles Verfahren zur verifizierten globalen Optimierung, PhD thesis, Bergische Universität GH Wuppertal, 1995.

    MATH  Google Scholar 

  22. J. E. Bertram, The effect of quantization in sampled feedback systems, Trans. AIEE, 77 (1958), pp. 177–182.

    Google Scholar 

  23. M. Berz and G. Hofstäster, Computation and application of Taylor polynomials with interval remainder bounds, Reliable Computing, 4 (1998), pp. 83–97.

    Article  MathSciNet  MATH  Google Scholar 

  24. G. Birkhoff, Lattice Theory, AMS Colloquium Public., 25, AMS, New York, 1940.

    Google Scholar 

  25. G. Birkhoff and R. S. Varga, Discretization errors for well-set Cauchy problems: I, J. Math. and Phys., 44 (1965), pp. 1–23.

    MathSciNet  MATH  Google Scholar 

  26. Blagovest Sendov and G. Beer, Hausdorff Approximations, Kluwer, Dordrecht, Netherlands, 1990.

    Google Scholar 

  27. Blitz, Homepage.1998.

    Google Scholar 

  28. J. E. Bobrow, A direct minimization approach for obtaining the distance between convex polyhedra, The International Journal of Robotics Research, 8 (1989), pp. 65–76.

    Article  Google Scholar 

  29. K. Braune, Standard functions for real and complex point and interval arguments with dynamic accuracy, Computing, Suppl., (1988), pp. 159–184.

    Google Scholar 

  30. R. P. Brent, Algorithm 524: MP, a FORTRAN multiple-precision arithmetic package, ACM Trans. Math. Software, 4 (1978), pp. 71–81.

    Article  Google Scholar 

  31. C. Brezinski and M. R. Zaglia, eds., Extrapolation Methods: Theory and Practice, Studies in Computational Mathematics, No. 2, North-Holland, 1991.

    Google Scholar 

  32. C. Brezinski, A general extrapolation procedure revisited, Advances Comput. Math., 2 (1994), pp. 461–477.

    MathSciNet  MATH  Google Scholar 

  33. B. P. Buckles and F. Petry, Genetic Algorithms, IEEE Computer Society Press, 1992.

    Google Scholar 

  34. A. Bunse-Gerstner, R. Byers, and V. MEHRMANN, Numerical methods for algebraic Riccati equations,in Lecture Notes of the Workshop on “The Riccati Equation in Control, Systems, and Signals” (Como, Italy), S. Bittanti, ed., Pitagora Editrice, Bologna, 1989, pp. 107115.

    Google Scholar 

  35. R. G. Burger and R. K. Dybvig, Printing floating point numbers quickly and accurately, Sigplan Notices, 31 (1996), pp. 108–116.

    Article  Google Scholar 

  36. B. F. Caviness and J. R. Johnson, eds., Quantifier Elimination and Cylindrical Algebraic Decomposition, Texts and Monographs in Symbolic Computation, Springer-Verlag, Berlin, 1998.

    Google Scholar 

  37. L. Chen, W. Q. Huang, and E. M. Song, A fast algorithm for computing the distance between two convex polyhedra, Math. J. Chinese Univ., 16 (1994), pp. 345–359.

    MathSciNet  MATH  Google Scholar 

  38. P. Chin, R. M. Corless, and G. F. Corliss, Globsol case study: Inexact greatest common denominators, Technical Report, Marquette University Department of Mathematics, Statistics, and Computer Science, Milwaukee, Wisc., 1998.

    Google Scholar 

  39. P. Chin, Optimization strategies for the approximate GCD problem, in Proceedings of the 1998 International Symposium on Symbolic and Algebraic Computation, O. Gloor, ed., New York, 1998, ACM Press, pp. 228–235.

    Chapter  Google Scholar 

  40. D. Chiriaev, Framework for reliable computing in Java(TM) programming language. Preprint., 1998.

    Google Scholar 

  41. D. Chiriaev and G. W. Walster, Interval arithmetic specification. 1998.

    Google Scholar 

  42. P. G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978.

    MATH  Google Scholar 

  43. J. C. Cleary, Logical arithmetic, Future Computing Systems, 2 (1987), pp. 125–149.

    Google Scholar 

  44. L. Collatz, Funktionalanalysis and Numerische Mathematik, Springer-Verlag, Berlin, 1964.

    Book  Google Scholar 

  45. L. Collatz, Differentialgleichungen, 6. Aufl. Teubner, Stuttgart, 1981.

    Google Scholar 

  46. H. Collavizza, F. Delobel, and M. Rueher, A note on partial consistencies over continuous domains solving techniques, in Proceedings of the Fourth International Conference on Principles and Practice of Constraint Programming (CP ‘88), Lecture Notes in Computer Science, No. 1520, Berlin, 1998, Springer-Verlag.

    Google Scholar 

  47. G. E. Collins, Quantifier elimination for the elementary theory of real closed fields by cylindrical algebraic decomposition, in Automata Theory and Formal Languages, H. Brakhage, ed., Lecture Notes in Computer Science, No. 33, Springer-Verlag, Berlin, 1975, pp. 134–183.

    Google Scholar 

  48. G. E. Collins and H. Hong, Partial cylindrical algebraic decomposition for quantifier elimination, J. Symbolic Comp., 12 (1991), pp. 299–328.

    Article  MathSciNet  MATH  Google Scholar 

  49. A. Connell and R. M. Corless, An experimental interval arithmetic package in Maple, Interval Computations, 2 (1993), pp. 120–134.

    Google Scholar 

  50. R. M. Corless, Cofactor iteration, Sigsam Bulletin: Communications in Computer Algebra, 30 (1996), pp. 34–38.

    Google Scholar 

  51. G. F. Corliss, Industrial applications of interval techniques, in Computer Arithmetic and Self-Validating Numerical Methods, C. Ullrich, ed., Notes and Reports in Mathematics in Science and Engineering, No. 7, Academic Press, New York, 1990, pp. 73–90.

    Google Scholar 

  52. G. F. Corliss, Comparing software packages for interval arithmetic. Presented at SCAN ‘83, Vienna, 1993.

    Google Scholar 

  53. G. F. Corliss, SCAN-98 collected bibliography, in Developments in Reliable Computing, T. Csendes, ed., Kluwer, Dordrecht, Netherlands, 1999, pp. 383–402.

    Google Scholar 

  54. G. F. Corliss and R. B. Kearfott, Rigorous global search: Industrial applications, in Developments in Reliable Computing, T. Csendes, ed., Kluwer, Dordrecht, Netherlands, 1999, pp. 1–16.

    Google Scholar 

  55. G. F. Corliss and L. B. Rall, Adaptive, self-validating quadrature, SIAM J. Sci. Stat. Comput., 8 (1987), pp. 831–847.

    Article  MathSciNet  MATH  Google Scholar 

  56. G. F. Corliss, Computing the range of derivatives,in Computer Arithmetic, Scientific Computation, and Mathematical Modelling, E. W. Kaucher, S. M. Markov, and G. Mayer, eds., vol. 12 of IMACS Annals on Computing and Applied Mathematics, J. C. Baltzer, Basel, 1991, pp. 195212.

    Google Scholar 

  57. G. F. Corliss and R. Rihm, Validating an a priori enclosure using high-order Taylor series, in Scientific Computing and Validated Numerics: Proceedings of the International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics–SCAN ‘85, G. Alefeld, A. Frommer, and B. Lang, eds., Akademie Verlag, Berlin, 1996, pp. 228–238.

    Google Scholar 

  58. G. E. Coxson, The P-matrix problem is co-NP-complete, Mathematical Programming, 64 (1994), pp. 173–178.

    Article  MathSciNet  Google Scholar 

  59. T. Csendes, ed., Developments in Reliable Computing, Kluwer, Dordrecht, Netherlands, 1999.

    MATH  Google Scholar 

  60. J. Daniels, S. Ranjit, R. B. Kearfott, and G. F. Corliss, Globsol case study: Currency trading (Swiss Bank Corp.), Technical Report, Department of Mathematics, Statistics and Computer Science, Marquette University, Milwaukee, Wisc., 1998.

    Google Scholar 

  61. G. Darboux, Sur les dèveloppements en série des fonctions d’une seule variable,J. des Mathématique pures et appl., (1876), pp. 291–312. 3ème série, t. II.

    Google Scholar 

  62. E. Davis, Constraint propagation with interval labels, Journal of Artificial Intelligence, 32 (1987), pp. 281–331.

    Article  Google Scholar 

  63. P. J. Davis and P. Rabinowitz, Methods of Numerical Integration, Academic Press, New York, 2nd ed., 1984.

    Google Scholar 

  64. J. P. Delahaye, Optimalité du procédé 8 2 d’Aitken pour l’accélération de la convergence linéaire, Rairo, Anal. Numér., 15 (1981), pp. 321–330.

    Google Scholar 

  65. J. P. Delahaye and B. Germain-Bonne, Résultats négatifs en accélération de la convergence, Numer. Math., 35 (1980), pp. 443–457.

    MathSciNet  MATH  Google Scholar 

  66. N. S. Dimitrova and S. M. Markov, On the interval-arithmetic presentation of the range of a class of monotone functions of many variables, in Computer Arithmetic, Scientific Computation and Mathematical Modelling, E. W. Kaucher, S. M. Markov, and G. Mayer, eds., J. C. Baltzer, Basel, 1991, pp. 213–228.

    Google Scholar 

  67. N. S. Dimitrova, A validated Newton type method for nonlinear equations, Interval Computation, 2 (1994), pp. 27–51.

    MathSciNet  Google Scholar 

  68. N. S. Dimitrova, Verified computation of fast decreasing polynomials, in Developments in Reliable Com- puting, T. Csendes, ed., Kluwer, Dordrecht, Netherlands, 1999, pp. 229–240. Also Reliable Computing 5/3 (1999), pp. 229–240.

    Google Scholar 

  69. N. S. Dimitrova, S. M. Markov, and E. Popova, Extended interval arithmetics: New results and applications,in Computer Arithmetic and Enclosure Methods, L. Atanassova and J. Herzberger, eds., Amsterdam, 1992, North-Holland, pp. 225–232.

    Google Scholar 

  70. T. A. Diverio, Uso efetivo da matematica intervalar em supercomputadores vetoriais,in Porto Alegre: Cpgcc da UFRGS, 1995, p. 291. Tese de doutorado.

    Google Scholar 

  71. T. A. Diverio and Et AL., Libavla Biblioteca de rotinas intervalares -Manual de utilizacao, in Porto Alegre: CPGCC da UFRGS, 1995, p. 350.

    Google Scholar 

  72. T. A. Diverio, U. A. L. Fernandes, and D. M. Claudio, Errors in vector processing and the libavia library, Reliable Computing, 2 (1996), pp. 103–110.

    Article  MATH  Google Scholar 

  73. T. A. Diverio, P. O. A. Navaux, D. M. Claudio, C. A. Hölbig, R. L. Sagula, and U. A. L. Fernandes, High performance with high accuracy laboratory, Revista de Informatica Teorica e Aplicada, RITA, Porto Alegre: Informaatica da UFRGS, 3 (1997), pp. 3554.

    Google Scholar 

  74. D. Dobkin, J. Hershberger, D. Kirkpatrick, and S. Suri, Computing the intersection–depth of polyhedra, Algorithmica, 9 (1993), pp. 528–533.

    Article  MathSciNet  Google Scholar 

  75. D. Dobkin and D. Kirkpatrick, Determining the separation of preprocessed polyhedra — A unified approach, in Automata, Languages and Programming (Coventry, 1990), Lecture Notes in Computer Science, No. 443, Springer-Verlag, New York, 1990, pp. 400–413.

    Chapter  Google Scholar 

  76. J. J. Dongarra, Performance of various computers using standard linear equations software. 1997.

    Google Scholar 

  77. J. J. Dongarra, J. J. Du Croz, I. S. Duff, and S. J. Hammarling, A set of level 3 basic linear algebra subprograms, ACM Trans. Math. Software, 16 (1990), pp. 1–17.

    Article  MATH  Google Scholar 

  78. J. J. Dongarra, J. J. Du Croz, S. J. Hammarling, and R. J. Hansen, An extended set of Fortran basic linear algebra subprograms, ACM Trans. Math. Software, 14 (1990), pp. 117.

    Google Scholar 

  79. R. Dunay and I. Kollar, MATLAB-based analysis of roundoff noise, in Developments in Reliable Computing, T. Csendes, ed., Kluwer, Dordrecht, Netherlands, 1999, pp. 373–382.

    Google Scholar 

  80. R. Dunay, I. Kollar, and B. Widrow, Dithering for floating point number representation, in 1st International On-Line Workshop (Prague, Czech Republic, Mar. 1998 ), J. Holub and R. Smid, eds., 1998.

    Google Scholar 

  81. E. Dyllong, W. Luther, and W. Otten, An accurate distance-calculation algorithm for convex polyhedra, in Developments in Reliable Computing, T. Csendes, ed., Kluwer, Dordrecht, Netherlands, 1999, pp. 241–254. Also Reliable Computing 5/3 (1999), pp. 241–254.

    Google Scholar 

  82. H. Edelsbrunner, Algorithms in Combinatorial Geometry, Monographs on Theoretical Computer Science, No. 10, Springer-Verlag, Berlin, 1987.

    Google Scholar 

  83. H. Edelsbrunner EGCS, egcs project homepage., 1998.

    Google Scholar 

  84. B. L. Ehle, On Padé approximations to the exponential function and A-stable methods for the numerical solution of initial value problems, Siam J. Math. Anal., 4 (1973), pp. 671–680.

    Google Scholar 

  85. P. Eijgenraam, The Solution of Initial Value Problems Using Interval Arithmetic, Mathematical Centre Tracts, No. 144, Stichting Mathematisch Centrum, Amsterdam, 1981.

    Google Scholar 

  86. L. Elsner and T. Szulc, Block p-matrices, Linear and Multilinear Algebra, 44 (1998), pp. 1–12.

    Article  MathSciNet  MATH  Google Scholar 

  87. J. S. Ely, The VPI software package for variable precision interval arithmetic, Interval Computations, 2 (1993), pp. 135–153.

    Google Scholar 

  88. W. H. Enright, T. E. Hull, and B. Lindberg, Comparing numerical methods for stiff systems of ODEs, BIT, 15 (1975), pp. 10–48.

    Article  MATH  Google Scholar 

  89. M. D. Ercegovac, T. LANG, J.-M. Muller, and A. Tisserand, Reciprocation, square root, inverse square root, and some elementary functions using small multipliers, Technical Report RR97–47, LIP, École Normale Supérieure de Lyon, November 1997.

    Google Scholar 

  90. A. Facius, The need for higher precision in solving large sparse linear systems, in Developments in Reliable Computing, T. Csendes, ed., Kluwer, Dordrecht, Netherlands, 1999, pp. 1730.

    Google Scholar 

  91. B. Faltings, Arc-consistency for continuous variables, Artificial Intelligence, 65 (1991), pp. 363–376.

    Google Scholar 

  92. P. M. Farmwald, High bandwidth evaluation of elementary functions, in Proceedings of the 5th IEEE Symposium on Computer Arithmetic, K. S. Trivedi and D. E. Atkins, eds., Los Alamitos, CA, 1981, IEEE Computer Society Press.

    Google Scholar 

  93. X. Feng, R. Yang, Y. YAN, Y. Zhu, G. F. Corliss, and R. B. Kearfott, Globsol case study: Parameter optimization for the eddy current compensation of MRI coils (General Electric Medical), Technical Report, Department of Mathematics, Statistics and Computer Science, Marquette University, Milwaukee, Wisc., 1998.

    Google Scholar 

  94. A. Fiat, R. Karp, M. Luby, L. Mcgeoch, D. Sleator, and N. E. Young, Competitive paging algorithms, J. Algorithms, 12 (1991), pp. 685–699.

    Article  MATH  Google Scholar 

  95. M. Fiedler, Special Matrices and Their Applications in Numerical Mathematics, Nijhof, Dordrecht, 1986.

    Book  MATH  Google Scholar 

  96. G. Freiling and G. Jank, Non-symmetric matrix Riccati equations, J. Analysis Appl., 14 (1995), pp. 259–284.

    MathSciNet  MATH  Google Scholar 

  97. E. C. Freuder, Synthesizing constraint expressions, Communications of the ACM, 21 (1978), pp. 958–966.

    Article  Google Scholar 

  98. F. Fritz, Development of a finite element analysis program based on interval arithmetic, master’s thesis, Marquette University Department of Mathematics, Statistics, and Computer Science, Milwaukee, Wisc., May 1999.

    Google Scholar 

  99. F. Fritz, P. Thalacker, G. F. Corliss, and R. B. Kearfott, Globsol User Guide,Technical Report, Department of Mathematics, Statistics and Computer Science, Marquette University, Milwaukee, Wiscde.

    Google Scholar 

  100. A. Frommer, Lösung linearer Gleichungssysteme auf Parallelrechnern, Vieweg-Verlag, Wiesbaden, 1990.

    Book  MATH  Google Scholar 

  101. A. Frommer and P. MAASS, Fast CG-based methods for Thikonov-Phillips regularization,SIAM J. Sci. Comp., (to appear).

    Google Scholar 

  102. A. Frommer and A. Weinberg, Verified error bounds for linear systems through the Lanczos process, in Developments in Reliable Computing, T. Csendes, ed., Kluwer, Dordrecht, Netherlands, 1999, pp. 255–268. Also Reliable Computing 5/3 (1999), pp. 255–268.

    Google Scholar 

  103. E. Garderes and A. Trepat, Fundamentals of SIGLA, an interval computing system over the completed set of intervals, Computing, 24 (1980), pp. 161–179.

    Article  MathSciNet  Google Scholar 

  104. E. Gardenes, A. Trepat, and H. Mielgo, Present perspective of the SIGLA interval system, Freiburger Intervall-Berichte, 82 (1982), pp. 1–65.

    Google Scholar 

  105. D. M. Gay, Correctly rounded binary-decimal and decimal-binary conversions, Numerical Analysis Manuscript 90–10, ATandT Bell Laboratories, November 1990.

    Google Scholar 

  106. E. G. Gilbert, D. W. Johnson, and S. S. Keerthi, A fast procedure for computing the distance between complex objects in three-dimensional space, IEEE Journal of Robotics and Automation, 4 (1988), pp. 193–203.

    Article  Google Scholar 

  107. V. Girault and P. A. Raviart, Finite Element Approximation of the Navier-Stokes Equations, Springer-Verlag, Berlin, 1986.

    Book  Google Scholar 

  108. G. Golub and G. Meurant, Matrices, moments and quadrature, in Numerical Analysis 1993 (Dundee 1993), Pitman Res. Notes Math., No. 302, Longman Sci. Tech., Harlow, 1994.

    Google Scholar 

  109. G. Golub, Matrices, moments and quadrature II. How to compute the error in iterative methods, BIT, 37 (1997), pp. 687–705.

    Article  MathSciNet  MATH  Google Scholar 

  110. G. Golub and J. H. Welsch, Calculation of Gauss quadrature rules, Math. Comp., 23 (1969), pp. 221–230.

    Article  MathSciNet  MATH  Google Scholar 

  111. G. H. Golub and C. F. VAN Loan, Matrix Computations, Johns Hopkins University Press, Baltimore, 3rd ed., 1996.

    Google Scholar 

  112. S. Gottschalk, Separating axis theorem, Technical Report TR96–024, Department of Computer Science, UNC Chapel Hill, 1996.

    Google Scholar 

  113. L. Granvilliers, On the combination of box-consistency and hull-consistency, in Proceedings of the Workshop ECAI on Non Binary Constraints ( Brighton, Aug., 1998 ), 1998.

    Google Scholar 

  114. J. H. Gray and L. B. Rall, INTE: A Univac 1108/1110 program for numerical integration with rigorous error estimation, MRC Technical Summary Report No. 1428, Mathematics Research Center, University of Wisconsin - Madison, 1975.

    Google Scholar 

  115. A. Greenbaum, Iterative Methods for Solving Linear Systems, Frontiers in Applied Mathematics, No. 17, SIAM, Philadelphia, 1997.

    Google Scholar 

  116. R. Gregory and D. Karney, A Collection of Matrices for Testing Computational Algorithms, Wiley, New York, 1969.

    Google Scholar 

  117. A. Griewank, ODE solving via automatic differentiation and rational prediction, in Numerical Analysis 1995, D. F. Griffiths and G. A. Watson, eds., Pitman Research Notes in Mathematics Series, No. 344, Addison-Wesley Longman, 1996.

    Google Scholar 

  118. A. Griewank, G. F. Corliss, P. Henneberger, G. Kirlinger, F. A. Potra, and H. J. Stetter, High-order stiff ODE solvers via automatic differentiation and rational prediction, in Numerical Analysis and Its Applications, Lecture Notes in Computer Science, No. 1196, Springer, Berlin, 1997, pp. 114–125.

    Chapter  Google Scholar 

  119. A. Griewank, D. Juedes, and J. Utke, ADOL-C, a package for the automatic differentiation of algorithms written in C/C++, ACM Trans. Math. Software, 22 (1996), pp. 131–167.

    Article  MATH  Google Scholar 

  120. A. Griewank, J. Utke, and A. Walther, Evaluating higher derivative tensors by forward propagation of univariate Taylor series, Preprint IOKOMO-09–97t, TU Dresden, Inst. of Scientific Computing, 1997. Revised June 1998.

    Google Scholar 

  121. E. Hairer, S. P. Norsett, and G. Wanner, Solving Ordinary Differential Equations I. Nonstiff Problems, Computational Mechanics, No. 8, Springer-Verlag, Berlin, 2nd revised ed., 1993.

    Google Scholar 

  122. R. Hammer, M. Hocks, U. Kulisch, and D. Ratz, Numerical Toolbox for Verified Computing I: With Algorithms and Pascal-XSC Programs, Springer-Verlag, Berlin, 1994.

    Google Scholar 

  123. R. Hammer, M. Hocks, C++ Toolbox for Verified Computing I: Basic Numerical Problems: Theory, Algorithms, and Programs, Springer-Verlag, Berlin, 1995.

    MATH  Google Scholar 

  124. E. R. Hansen, Global Optimization Using Interval Analysis, Marcel Dekker, New York, 1992.

    MATH  Google Scholar 

  125. P. Hansen, Regularization tool, a MATLAB package for the analysis and solution of discrete ill-posed problems; version 2.0 for MATLAB 4.0, Technical Report 92–03, UNIC, 1992.

    Google Scholar 

  126. H. Hassler and N. Takagi, Function evaluation by table look-up and addition, in Proceedings of the 12th IEEE Symposium on Computer Arithmetic (Bath, UK, July 1995), S. Knowles and W. McAllister, eds., Los Alamitos, CA, 1995, IEEE Computer Society Press.

    Google Scholar 

  127. G. L. Haviland and A. A. Tuszynski, A CORDIC arithmetic processor chip, IEEE Trans. on Computers, C-29 (1980), pp. 68–79.

    Google Scholar 

  128. G. Heindl, Zur Einschließung der Werte von Peanofunktionalen, Z. angew. Math. Mech., 75 (1995), pp. 637–638.

    Google Scholar 

  129. G. Heindl, A representation of the interval hull of a tolerance polyhedron describing inclusions of function values and slopes,in Developments in Reliable Computing, T. Csendes, ed., Kluwer, Dordrecht, Netherlands, 1999, pp. 269–278. Also Reliable Computing 5/3 (1999), pp. 269278.

    Google Scholar 

  130. F. D. Helene Collavizza and M. Rueher, Comparing partial consistencies, in Developments in Reliable Computing, T. Csendes, ed., Kluwer, Dordrecht, Netherlands, 1999, pp. 213228. Also Reliable Computing 5/3 (1999), pp. 213–228.

    Google Scholar 

  131. P. Henrici, Circular Arithmetic and the Determination of Polynomial Zeros, Lecture Notes, No. 228, Springer, Heidelberg, 1971.

    Google Scholar 

  132. C. Hermite, Extrait d’une lettre de M. Ch. Hermite à M. Borchardt sur la formule d’interpolation de Lagrange, J. de Crelle, 84 (1878), p. 70. Oeuvres, tome III, p. 432–443.

    Google Scholar 

  133. M. R. Hestenes and E. Stiefel, Methods of conjugate gradients for solving linear systems, Journal of Research of the National Bureau of Standards, 49 (1952), pp. 409–436.

    Article  MathSciNet  MATH  Google Scholar 

  134. W. Hofschuster and W. Krämer, A fast public domain interval library in ANSI C, in Proceedings of the 15th IMACS World Congress on Scientific Computation, Modelling and Applied Mathematics, Vol. 2, A. Sydow, ed., 1997, pp. 395–400.

    Google Scholar 

  135. O. Holzmann, B. Lang, and H. Schütt, Newton’s constant of gravitation and verified numerical quadrature, Reliable Computing, 2 (1996), pp. 229–239.

    Article  MATH  Google Scholar 

  136. H. Hong, An improvement of the projection operator in cylindrical algebraic decomposition, in Proceedings of ISSAC 1990, 1990, pp. 261–264.

    Google Scholar 

  137. H. Hong and V. Stahl, Safe starting regions by fixed points and tightening, Computing, 53 (1994), pp. 323–335.

    Article  MathSciNet  MATH  Google Scholar 

  138. J. Hormigo, J. Villalba, and E. L. Zapata, A hardware approach to interval arithmetic for sine and cosine functions, in Developments in Reliable Computing, T. Csendes, ed., Kluwer, Dordrecht, Netherlands, 1999, pp. 31–42.

    Google Scholar 

  139. R. Horst and P. M. Pardalos, Handbook of Global Optimization, Kluwer, Dordrecht, Netherlands, 1995.

    Google Scholar 

  140. E. G. Houghton, R. F. Emnett, J. D. Factor, and C. L. Sabharwal, Implementation of a divide-and-conquer method for intersection of parametric surfaces, Computer Aided Geometric Design, 2 (1985), pp. 173–183.

    Article  MATH  Google Scholar 

  141. Y. H. Hu, The quantization effects of the CORDIC algorithm., IEEE Trans. on Signal Processing, 40 (1992), pp. 834–844.

    Article  MATH  Google Scholar 

  142. E. Huber, Intersecting general parametric surfaces using bounding volumes,in Tenth Canadian Conference on Computational Geometry - CCCG ‘88,1998, pp. 52–54.

    Google Scholar 

  143. E. Huber and W. Barth, Surface-to-surface intersection with complete and guaranteed results, in Developments in Reliable Computing, T. Csendes, ed., Kluwer, Dordrecht, Netherlands, 1999, pp. 189–202.

    Google Scholar 

  144. D. Husung, ABACUS-Programmierwerkzeug mit hochgenauerArithmetikfirAlgorithmen mit verifizierten Ergebnissen, diplomarbeit, Universität Karlsruhe, 1988.

    Google Scholar 

  145. D. Husung, Precompiler for Scientific Computation (TPX), Technical Report 91.1, Inst. f. Infor- matik III, TU Hamburg-Harburg, 1989.

    Google Scholar 

  146. E. Hyvónen, Constraint reasoning based on interval arithmetic: The tolerance propagation approach, Artificial Intelligence, 58 (1992), pp. 71–112.

    Article  MathSciNet  Google Scholar 

  147. IBM, High–Accuracy Arithmetic Subroutine Library (ACRITH); General Information Manual, 3rd Edition, GC 33–6163–02; Program Description and User’s Guide, SC 33–6164–02,IBM Deutschland GmbH, 3rd ed., 1986.

    Google Scholar 

  148. IEEE, IEEE standard equipment requirements and measurement techniques (IEEE/ANSI 7341985), Technical Report, IEEE, 1985.

    Google Scholar 

  149. M. Iri, Automatic differentiation, Bull. Jap. Soc. Industrial and Applied Mathematics, 3 (1993).

    Google Scholar 

  150. M. Iri, Guaranteed accuracy and fast automatic differentiation, KITE Journal of Electronics Engineering, 4 (1993), pp. 34–40.

    Google Scholar 

  151. M. Iri, The role of automatic differentiation in nonlinear analysis and high-quality computa- tion, Technical Report TRISE 96–05, Dept. of Information and System Engineering, Faculty of Science and Engineering, Chuo University, Tokyo, Japan, 1996.

    Google Scholar 

  152. K. G. Ivanov and V. Totik, Fast decreasing polynomials, Constructive Approx., 6 (1990), pp. 1–20.

    Article  MathSciNet  MATH  Google Scholar 

  153. C. Jansson, Interval linear systems with symmetric matrices, skew-symmetric matrices and dependencies in right hand side, Computing, 46 (1991), pp. 265–274.

    Article  MathSciNet  MATH  Google Scholar 

  154. C. Jansson, A global optimization method using interval arithmetic, IMACS Annals of Computing and Applied Mathematics, (1992).

    Google Scholar 

  155. C. Jansson, On self-validating methods for optimization problems, in Topics in Validated Computa- tions: Proceedings of the IMACS-GAMM International Workshop on Validated Computations (Oldenburg, 30 Aug.–3 Sept., 1993), J. Herzberger, ed., Studies in Computational Mathematics, No. 5, Amsterdam, 1994, North-Holland/Elsevier, pp. 381–439.

    Google Scholar 

  156. C. Jansson, Construction of convex lower and concave upper bound functions, Bericht 98.1, For- schungsschwerpunktes Informations-and Kommunikationstechnik der Technischen Universität Hamburg-Harburg, März 1998.

    Google Scholar 

  157. M. Jirstrand, Constructive Methods for Inequality Constraints in Control,PhD thesis, Linkoping Studies in Science and Technology, 1998. Dissertations, No. 527.

    Google Scholar 

  158. C. R. Johnson and M. J. Tsatsomeros, Convex sets of nonsingular and P-matrices, Linear and Multilinear Algebra, 38 (1995), pp. 233–240.

    Article  MathSciNet  MATH  Google Scholar 

  159. W. Kahan, The baleful effect of computer benchmarks upon applied mathematics, physics and, 1998.

    Google Scholar 

  160. E. W. Kaucher, Algebraische Erweiterungen der Intervallrechnung unter Erhaltung der Ordnungs-and Verbandstrukturen, Computing Suppl., 1 (1977), pp. 65–79.

    Article  Google Scholar 

  161. E. W. Kaucher, Interval analysis in the extended interval space IR, Computing, Suppl., 2 (1980), pp. 33–49.

    MathSciNet  Google Scholar 

  162. R. B. Kearfott, A Fortran 90 environment for research and prototyping of enclosure algorithms for nonlinear equations and global optimization, ACM Trans. Math. Software, 21 (1995), pp. 63–78.

    Article  MATH  Google Scholar 

  163. R. B. Kearfott, A review of techniques in the verified solution of constrained global optimization problems, in Applications of Interval Computations, R. B. Kearfott and V. Kreinovich, eds., Kluwer, Dordrecht, Netherlands, 1996, pp. 23–59.

    Chapter  Google Scholar 

  164. R. B. Kearfott, Rigorous Global Search: Continuous Problems, Kluwer, Dordrecht, Netherlands, 1996.

    Google Scholar 

  165. R. B. Kearfott, A specific proposal for interval arithmetic in Fortran. 1996.

    Google Scholar 

  166. R. B. Kearfott, M. Dawande, K. S. Du, and C. Hu, INTLIB: A portable Fortran 77 interval elementary function library, Interval Computing, 3 (1992), pp. 96–105.

    MathSciNet  Google Scholar 

  167. R. B. Kearfott, Algorithm 737: INTLIB: A portable Fortran 77 interval standard library, ACM Trans. Math. Software, 20 (1994), pp. 447–459.

    Article  MATH  Google Scholar 

  168. R. B. Kearfott and K. S. Du, The cluster problem in multivariate global optimization, J. of Global Optimization, 5 (1994), pp. 253–265.

    Article  MathSciNet  MATH  Google Scholar 

  169. R. B. Kearfott and V. Kreinovich,Applications of Interval Computations, Kluwer, Dordrecht, Netherlands, 1996.

    Google Scholar 

  170. R. B. Kearfott and M. Novoa, Algorithm 681: INTBIS: A portable interval Newton/bisection package, ACM Trans. Math. Software, 16 (1990), pp. 152–157.

    Article  MATH  Google Scholar 

  171. G. Kedem, Automatic differentiation of computer programs, ACM Trans. Math. Software, 6 (1980), pp. 150–165.

    Article  Google Scholar 

  172. J. B. Keiper and D. Withoff, Numerical computation in Mathematica, in Course Notes, Mathematica Conference, 1992.

    Google Scholar 

  173. B. Kelling, Geometrische Untersuchungen zur eigenschränkte Lösungsmenge Intervallgleichungssysteme, ZAMM, 74 (1994), pp. 625–628.

    Article  MathSciNet  MATH  Google Scholar 

  174. R. Kelnhoffer, Applications of Interval Methods to Parametric Set Estimation from Bounded Error Data, PhD thesis, Marquette University Department of Electrical and Cornputer Engineering, 1997.

    Google Scholar 

  175. R. Klatte, U. Kulisch, M. Neaga, D. Ratz, and C. Ullrich, PASCAL-XSC, Sprachbeschreibung mit Beispielen, Springer-Verlag, Berlin, 1991.

    MATH  Google Scholar 

  176. R. Klatte, PASCAL-XSC, Language Reference with Examples, Springer-Verlag, Berlin, 1992.

    MATH  Google Scholar 

  177. R. Klatte, U. Kulisch, A. Wiethoff, C. Lawo, and M. Rauch, C-XSC, A C++ Class Library for Extended Scientific Computing, Springer-Verlag, Berlin, 1993.

    MATH  Google Scholar 

  178. R. Klatte and C. P. Ullrich, Complex sector arithmetic, Computing, 24 (1980).

    Google Scholar 

  179. S. C. Kleene, Mathematical Logic, Wiley, New York, 1967.

    MATH  Google Scholar 

  180. O. Knüppel, BIAS - basic interval arithmetic subroutines, Technical Report 93.3, Inst. f. Informatik III, TU Hamburg-Harburg, July 1993.

    Google Scholar 

  181. O. Knüppel, PROFIL/BIAS -A fast interval library, Computing, 53 (1994), pp. 277–287.

    Article  MathSciNet  MATH  Google Scholar 

  182. O. Knüppel, PROFIL/BIAS and extensions, version 2.0, Technical Report, Inst. f. Informatik III, TU Hamburg-Harburg, 1998.

    Google Scholar 

  183. L. V. Kolev, Interval Methods for Circuit Analysis, World Scientific, 1993.

    Google Scholar 

  184. I. Kollar, Statistical theory of quantization, Doct. Sci. Thesis, Hungarian Academy of Sciences, Budapest, 1996.

    Google Scholar 

  185. B. Kolodzieiczak and T. Szulc, Convex sets of full rank matrices, in Developments in Reliable Computing, T. Csendes, ed., Kluwer, Dordrecht, Netherlands, 1999, pp. 359–364.

    Google Scholar 

  186. B. Kolodzieiczak, Convex combinations of matrices - Full rank characterizations,Linear Algebra Appl., (to appear).

    Google Scholar 

  187. K. Kota and J. R. Cavallaro, Numerical accuracy and hardware tradeoffs for CORDIC arithmetic for special purpose processors, IEEE Trans. on Computers, 42 (1993), pp. 769–779.

    Article  Google Scholar 

  188. W. Kratz and E. Stickel, Numerical solution of matrix polynomial equations by Newton’s method, IMA J. Numer. Anal., 7 (1987), pp. 355–369.

    Article  MathSciNet  MATH  Google Scholar 

  189. R. Krawczyk, Newton-Algorithmen zur Bestimmung von Nullstellen mit Fehlerschranken, Computing, 4 (1969), pp. 187–201.

    Article  MATH  Google Scholar 

  190. R. Krier, Komplexe Kreisarithmetik, PhD thesis, Universität Karlsruhe, 1973.

    Google Scholar 

  191. F. Krückeberg, Ordinary differential equations, in Topics in Interval Analysis, E. R. Hansen, ed., Clarendon Press, Oxford, 1969, pp. 91–97.

    Google Scholar 

  192. D. Kuck and B. Kuhn, Kuck Associates, 1998.

    Google Scholar 

  193. W. Kühn, Rigorously computed orbits of dynamical systems without the wrapping effect, Computing, 61 (1998), pp. 47–67.

    Article  MathSciNet  MATH  Google Scholar 

  194. W. Kühn, Towards an optimal control of the wrapping effect, in Developments in Reliable Com- puting, T. Csendes, ed., Kluwer, Dordrecht, Netherlands, 1999, pp. 43–52.

    Google Scholar 

  195. U. W. Kulisch, ed., Wissenschaftliches Rechnen mit Ergebnisverifikation - Eine Einführung, Akademie Verlag, Berlin, and Vieweg Verlag, Wiesbaden, 1989.

    Google Scholar 

  196. U. W. Kulisch and W. L. Miranker, Computer Arithmetic in Theory and Practice, Academic Press, New York, 1981.

    MATH  Google Scholar 

  197. U. W. Kulisch, A New Approach to Scientific Computation, Academic Press, New York, 1983.

    MATH  Google Scholar 

  198. U. W. Kulisch, The arithmetic of the digital computer: A new approach, SIAM Review, 28 (1986), pp. 1–40.

    Article  MathSciNet  MATH  Google Scholar 

  199. L. V. Kupriyanova, Inner estimation of the united solution set of interval linear algebraic system, Reliable Computing, 1 (1995), pp. 15–31.

    Article  MathSciNet  MATH  Google Scholar 

  200. O. Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach, 1969.

    Google Scholar 

  201. A. V. Lakeyev, Linear algebraic equations in Kaucher arithmetic, Reliable Computing, Supplement (Extended Abstracts of APIC ‘85: International Workshop on Applications of Interval Computations, El Paso, TX, Feb. 23–25, 1995 ), (1995), pp. 130–133.

    Google Scholar 

  202. A. V. Lakeyev, Computational complexity of estimation of the generalized solution sets to interval linear systems, in Proceedings of XI International Conference “Optimization Methods and Their Applications”(Baikal, July 5–12, 1998), Irkutsk, 1998, pp. 115–118.

    Google Scholar 

  203. A. V. Lakeyev, On existence and uniqueness of solutions of linear algebraic equations in Kaucher’s in- terval arithmetic, in Developments in Reliable Computing, T. Csendes, ed., Kluwer, Dordrecht, Netherlands, 1999, pp. 53–66.

    Google Scholar 

  204. J. D. Lambert, Computational Methods in Ordinary Differential Equations, Wiley, 1977.

    Google Scholar 

  205. C. Lanczos, An iteration method for the solution of the eigenvalue problem of linear differential and integral operators, J. Res. Nat. Bur. Standards, 45 (1950), pp. 255–282.

    Article  MathSciNet  Google Scholar 

  206. B. Lang, A comparison of subdivision strategies for verified multi-dimensional Gaussian quadrature, in Developments in Reliable Computing, T. Csendes, ed., Kluwer, Dordrecht, Netherlands, 1999, pp. 67–76.

    Google Scholar 

  207. D. Lasser, Kurven und Flächenverschneidungsmethoden, in Geometrische Verfahren der Graphischen Datenverarbeitung, J. L. Encarnaçäo, ed., Springer-Verlag, Berlin, 1990, pp. 6187.

    Google Scholar 

  208. C. Lawo, C XSC, A programming environment for verified scientific computing and numerical data processing, in Scientific Computing with Automatic Result Verification, E. Adams and U. Kulisch, eds., Academic Press, Orlando, Ra., 1992, pp. 71–86.

    Google Scholar 

  209. C. L. Lawson, R. J. Hanson, D. Kincaid, and F. T. Krogh, Algorithm 539: Basic linear algebra subprograms for Fortran usage,ACM Trans. Math. Software, 5 (1979), pp. 308325.

    Google Scholar 

  210. Y. Lebbah and O. Lhomme, Acceleration methods for numeric CSPs,in Proceedings of the Fifteenth National Conference on Artificial Intelligence (AAAI-98), Madison, WI, USA, July 26–30 1998, MIT Press, pp. 19–24.

    Google Scholar 

  211. Y. Lebbah, Prediction by extrapolation for interval tightening methods, in Developments in Reli- able Computing, T. Csendes, ed., Kluwer, Dordrecht, Netherlands, 1999, pp. 159–166.

    Google Scholar 

  212. J. H. M. Lee and M. H. Van Emden, Interval computation as deduction in CHIP, Journal of Logic Programming, 16 (1993), pp. 255–276.

    Article  MathSciNet  MATH  Google Scholar 

  213. V. Lefèvre, An algorithm that computes a lower bound on the distance between a segment and Z2, Research Report 97–18, Laboratoire de l’Informatique du Parallélisme, Lyon, France, June 1997.

    Google Scholar 

  214. V. Lefèvre, An algorithm that computes a lower bound on the distance between a segment and Z z, in Developments in Reliable Computing, T. Csendes, ed., Kluwer, Dordrecht, Netherlands, 1999, pp. 203–212.

    Google Scholar 

  215. V. Lefèvre, J.-M. Muller, and A. Tisserand, Towards correctly rounded transcendentals, in Proceedings of the 13th IEEE Symposium on Computer Arithmetic, Asilomar, USA, 1997, IEEE Computer Society Press, Los Alamitos, CA, 1997.

    Google Scholar 

  216. M. Lerch, Expression concepts in scientific computing, in Developments in Reliable Computing, T. Csendes, ed., Kluwer, Dordrecht, Netherlands, 1999, pp. 119–132.

    Google Scholar 

  217. M. Lerch and J. Wolff Von Gudenberg, Expression templates for dot product expressions, Reliable Computing, 5 (1999), pp. 69–80.

    Article  MathSciNet  MATH  Google Scholar 

  218. M. Lerch, Multiaspect interval types, in Developments in Reliable Computing, T. Csendes, ed., Kluwer, Dordrecht, Netherlands, 1999, pp. 365–372.

    Google Scholar 

  219. O. Lhomme, Consistency techniques for numeric CSPs,in Proceedings of International Joint Conference on Artificial Intelligence (IJCAI-93), R. Bajcsy, ed., Chambery, France, Aug. 1993, Morgan Kaufmann, pp. 232–238.

    Google Scholar 

  220. O. Lhomme and M. Rueher, Application des techniques CSP au raisonnement sur les intervalles, Revue d’intelligence Artificielle (Dunod), 11 (1997), pp. 283–312.

    MATH  Google Scholar 

  221. R. J. Lohner, A verified solver for linear systems with band structure. To be included in Toolbox for Verified Computing II.

    Google Scholar 

  222. R. J. Lohner, Enclosing the solutions of ordinary initial and boundary value problems, in Com- puter Arithmetic: Scientific Computation and Programming Languages, E. W. Kaucher, U. W. Kulisch, and C. Ullrich, eds., Wiley-Teubner Series in Computer Science, Stuttgart, 1987, pp. 255–286.

    Google Scholar 

  223. R. J. Lohner, Einschließung der Lösung gewöhnlicher Anfangs-and Randwertaufgaben and Anwendungen, PhD thesis, Universität Karlsruhe, 1988.

    Google Scholar 

  224. G. Ludyk, CAE von Dynamischen Systemen, Analyse, Simulation, Entwurf von Regelungsstemen, Springer-Verlag, Berlin, 1990.

    Book  Google Scholar 

  225. W. Luther and W. Otten, The complex arithmetic geometric mean and multiple precision matrix functions,in Scientific Computing and Validated Numerics: Proceedings of the International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics - SCAN ‘85, G. Alefeld, A. Frommer, and B. Lang, eds., Berlin, 1996, Akademie Verlag, pp. 52–58.

    Google Scholar 

  226. W. Luther, Verified calculation of the solution of algebraic Riccati equation, in Developments in Reliable Computing, T. Csendes, ed., Kluwer, Dordrecht, Netherlands, 1999, pp. 105–118.

    Google Scholar 

  227. A. Mackworth, Consistency in networks of relations, Journal of Artificial Intelligence, 8 (1977), pp. 99–118.

    Article  MATH  Google Scholar 

  228. S. M. Markov, Interval differential equations, in Interval Mathematics 1980, K. Nickel, ed., Academic Press, New York, 1980, pp. 145–164.

    Google Scholar 

  229. S. M. Markov, Some applications of extended interval arithmetic to interval iterations, Computing Suppl., 2 (1980), pp. 69–84.

    Article  Google Scholar 

  230. S. M. Markov, On the presentation of ranges of monotone functions using interval arithmetic, Interval Computations, 4 (1992), pp. 19–31.

    Google Scholar 

  231. S. M. Markov, On directed interval arithmetic and its applications, JUCS, 1 (1995), pp. 510–521.

    Google Scholar 

  232. S. M. Markov, On the algebraic pmperties of convex bodies and some applications. Preprint, 1998.

    Google Scholar 

  233. S. M. Markov, An iterative method for algebraic solution to interval equations, Applied Numerical Mathematics, 30 (1999), pp. 225–239.

    Article  MathSciNet  MATH  Google Scholar 

  234. S. M. Markov, On the algebraic properties of convex bodies and some applications,J. Convex Analy- sis, (submitted).

    Google Scholar 

  235. S. M. Markov and R. ALT, On the relation between stochastic and interval arithmetic. Preprint, 1998.

    Google Scholar 

  236. S. M. Markov and K. Okumura, The contribution of T. Sunaga to interval analysis and reliable computing, in Developments in Reliable Computing, T. Csendes, ed., Kluwer, Dordrecht, Netherlands, 1999, pp. 167–188.

    Google Scholar 

  237. Mathworks, Matlab User’s Manual, Version 5. 2, The MathWorks, Inc., Natick, Mass., 1998.

    Google Scholar 

  238. O. Mayer, Algebraische and metrische Strukturen in der Intervallrechnung and einige Anwendungen, Computing, 5 (1970), pp. 144–162.

    Article  MATH  Google Scholar 

  239. S. Mccallum, An improved projection for cylindrical algebraic decomposition, in Quantifier Elimination and Cylindrical Algebraic Decomposition, B. Caviness and J. Johnson, eds., Springer-Verlag, Berlin, 1988.

    Google Scholar 

  240. S. Mccallum, An improved projection for cylindrical algebraic decomposition of three dimensional space, J. Symbolic Comp., 5 (1988), pp. 141–161.

    Article  MathSciNet  MATH  Google Scholar 

  241. S. Mccallum, Solving polynomial strict inequalities using cylindrical algebraic decomposition, The Computer Journal, 36 (1993), pp. 432–438.

    Article  MathSciNet  MATH  Google Scholar 

  242. C. C. Mcgeoch, How to stay competitive, Amer. Math. Monthly, 101 (1994), pp. 897–901.

    Article  MathSciNet  MATH  Google Scholar 

  243. V. Mehrmann and E. Tan, Defect correction methods for the solution of algebraic Riccati equations, IEEE Trans. Automat. Control, AC-33 (1988), pp. 695–698.

    Google Scholar 

  244. M. Milanese, J. Norton, H. Piet-Lahanier, and E. Water, eds., Bounding Approaches to System Identification, Plenum Press, London, 1996.

    MATH  Google Scholar 

  245. D. S. Mitrinovie, J. E. Pelari6, and V. Volenec, Recent Advances in Geometric Inequalities, Kluwer, Dordrecht, Netherlands, 1989.

    Google Scholar 

  246. M. B. Monagan, K. O. Geddes, K. M. Heal, G. Labahn, and S. M. Vorkoetter, Maple V Programming Guide, Springer-Verlag, Berlin, 1998.

    Google Scholar 

  247. U. Montanari, Networks of constraints: Fundamental properties and applications to picture processing, Information Science, 7 (1974), pp. 95–132.

    Article  MathSciNet  MATH  Google Scholar 

  248. R. E. Moore, Interval Arithmetic and Automatic Error Analysis in Digital Computing, PhD thesis, Department of Computer Science, Stanford University, 1962.

    Google Scholar 

  249. R. E. Moore, The automatic analysis and control of error in digital computation based on the use of interval numbers, in Error in Digital Computation, Vol. I, L. B. Rall, ed., Wiley, New York, 1965, pp. 61–130.

    Google Scholar 

  250. R. E. Moore, Automatic local coordinate transformations to reduce the growth of error bounds in interval computation of solutions of ordinary differential equations, in Error in Digital Computation, Vol. II, L. B. Rall, ed., Wiley, New York, 1965, pp. 103–140.

    Google Scholar 

  251. R. E. Moore, Interval Analysis, Prentice Hall, Englewood Cliffs, N.J., 1966. German translation: Intervallanalyse, translated by D. Pfaffenzeller, R. Oldenburg, München, 1968.

    Google Scholar 

  252. A test for existence of solutions for non-linear systems, SIAM J. Numer. Anal., 4 (1977), pp. 611–615.

    Article  Google Scholar 

  253. R. E. Moore, Methods and Applications of Interval Analysis, SIAM, Philadelphia, Penn., 1979.

    Google Scholar 

  254. R. E. Moore, Reliability in Computing: The Role of Interval Methods in Scientific Computations, Academic Press, 1988.

    Google Scholar 

  255. J.-M. Muller, Elementary Functions: Algorithms and Implementations, Birkhaüser, Boston, 1997.

    Book  Google Scholar 

  256. J.-M. Muller, A few results on table-based methods, in Developments in Reliable Computing, T. Csendes, ed., Kluwer, Dordrecht, Netherlands, 1999, pp. 279–288. Also Reliable Computing 5/3 (1999), pp. 279–288.

    Google Scholar 

  257. K. Musch and G. Schumacher, Interval analysis for embedded systems, in Developments in Reliable Computing, T. Csendes, ed., Kluwer, Dordrecht, Netherlands, 1999, pp. 149–158.

    Google Scholar 

  258. N. C. Myers, Traits: A new and useful template technique, C++ Report, (1995).

    Google Scholar 

  259. M. T. Nakao, A numerical verification method for the existence of weak solutions for nonlinear boundary value problems, J. Math. Anal. Appl., 164 (1992), pp. 489–507.

    Article  MathSciNet  MATH  Google Scholar 

  260. M. T. Nakao, Solving nonlinear elliptic problems with result verification using an H-I type residual iteration, Computing, Suppl., 9 (1993), pp. 161–173.

    Google Scholar 

  261. M. T. Nakao, N. Yamamoto, and S. Kimura, On best constant in the optimal error estimates for the Hó-projection into piecewise polynomial spaces,J. Approximation Theory, (to appear).

    Google Scholar 

  262. M. T. Nakao, N. Yamamoto, and Y. Watanabe, Guaranteed error bounds for the finite element solutions of the Stokes problem,in Scientific Computing and Validated Numerics: Proceedings of the International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics - SCAN ‘85, G. Alefeld, A. Frommer, and B. Lang, eds., Berlin, 1996, Akademie Verlag, pp. 258–264.

    Google Scholar 

  263. M. T. Nakao, Constructive L2 error estimates for finite element solutions of the Stokes equations, Reliable Computing, 4 (1998), pp. 115–124.

    Article  MathSciNet  MATH  Google Scholar 

  264. M. T. Nakao, A posteriori and constructive a priori error bounds for finite element solutions of the Stokes equations, J. Comput. Appl. Math., 91 (1998), pp. 137–158.

    MATH  Google Scholar 

  265. N. S. Nedialkov, Computing Rigorous Bounds on the Solution of an Initial Value Problem for an Ordinary Differential Equation, PhD thesis, Department of Computer Science, University of Toronto, Toronto, Canada, M5S 3G4, February 1999.

    Google Scholar 

  266. N. S. Nedialkov and K. R. Jackson, An interval Hermite-Obreschkoff method for computing rigorous bounds on the solution of an initial value problem for an ordinary differential equation, in Developments in Reliable Computing, T. Csendes, ed., Kluwer, Dordrecht, Netherlands, 1999, pp. 289–310. Also Reliable Computing 5/3 (1999), pp. 289–310.

    Google Scholar 

  267. N. S. Nedialkov, K. R. Jackson, and G. F. Corliss, Validated solutions of initial value problems for ordinary differential equations,Appl. Math. Comp., (to appear).

    Google Scholar 

  268. A. Neumaier, A distributive interval arithmetic,Freiburger Intervall-Berichte, 82 (1982), pp. 31–38. Inst. f. Angewandte Mathematik, U. Freiburg i. Br.

    Google Scholar 

  269. A. Neumaier, Tolerance analysis with interval arithmetic, Freiburger Intervall-Berichte, 86 (1986), pp. 5–19.

    Google Scholar 

  270. A. Neumaier, Interval Methods for Systems of Equations, Cambridge University Press, Cambridge, 1990.

    MATH  Google Scholar 

  271. A. Neumaier, S. Dallwig, and H. Schichl, GLOPT-A program for constrained global optimization, in Developments in Global Optimization, I. Bomze et al., ed., Kluwer, Dordrecht, 1997, pp. 19–36.

    Google Scholar 

  272. N. Obreschkoff, Nist, Matrix market.

    Google Scholar 

  273. N. Obreschkoff, Neue Quadraturforneln, Abh. Preuss. Akad. Wiss. Math. Nat. Kl., 4 (1940).

    Google Scholar 

  274. N. Obreschkoff, Sur le quadrature mecaniques, Spisanie Bulgar. Akad. Nauk. (Journal of the Bulgarian Academy of Sciences), 65 (1942), pp. 191–289.

    Google Scholar 

  275. K. Okumura, An application of interval operations to electric network analysis,Bull. of the Japan Society for Industrial and Applied Mathematics, 3 (1993), pp. 15–27. In Japanese.

    Google Scholar 

  276. K. Okumura, Recent topic of circuit analysis - an application of interval arithmetic,Journal of System Control, 40 (1996), pp. 393–400. In Japanese.

    Google Scholar 

  277. K. Okumura, S. Saeki, and A. Kishima, On an improvement of an algorithm using interval analysis for solution of nonlinear circuit equations,Trans. of IECEJ, J69-A (1986), pp. 489–496. In Japanese.

    Google Scholar 

  278. W. J. Older and A. Velino, Extending Prolog with constraint arithmetic on real intervals, in Proc. of IEEE Canadian conference on Electrical and Computer Engineering, New York, 1990, IEEE Computer Society Press.

    Google Scholar 

  279. W. J. Older, Constraint arithmetic on real intervals, in Constraint Logic Programming: Selected Research, F. Benhamou and A. Colmerauer, eds., MIT Press, 1993, pp. 175–196.

    Google Scholar 

  280. J. M. Ortega and W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970.

    MATH  Google Scholar 

  281. C. C. Paige, The Computation of Eigenvalues and Eigenvectors of Very Large Sparse Matrices, PhD thesis, University of London, 1971.

    Google Scholar 

  282. B. Parlett, The Symmetric Eigenvalue Problem, Prentice-Hall, Englewood Cliffs, NJ, 1980.

    MATH  Google Scholar 

  283. M. Petrovich, Calculation with numerical intervals,Beograd, (1932). In Serbian, Serbian title: Racunanje sa brojnim razmacima.

    Google Scholar 

  284. L. S. Pontrjagin, Topological Groups, Princeton Univ. Press, Princeton, 1946.

    Google Scholar 

  285. E. Popova and C. Ullrich, Embedding directed intervals in Mathematica, Revista de Informatica Teorica e Applicada, 3 (1996), pp. 99–115.

    Google Scholar 

  286. J. E. Potter, Matrix quadratic solutions, J. SIAM Appl. Math., 14 (1966), pp. 496–501.

    Article  MathSciNet  MATH  Google Scholar 

  287. D. Priest, Fast table-driven algorithms for interval elementary functions, in Proceedings of the 13th Symposium on Computer Arithmetic (Pacific Grove, CA, July 6–9, 1997), IEEE Computer Society Press, New York, 1997, pp. 168–174.

    Google Scholar 

  288. Prologia, ProloglV Constraints Inside,Parc technologique de Luminy - Case 919 13288, Marseille cedex 09 (France), 1996.

    Google Scholar 

  289. S. Quinlan, Efficient distance computation between non-convex objects, in IEEE Intern. Conf. on Robotics and Automation, IEEE, 1994, pp. 3324–3329.

    Google Scholar 

  290. L. B. Rall, Automatic Differentiation: Techniques and Applications, Lecture Notes in Computer Science, No. 120, Springer-Verlag, Berlin, 1981.

    Google Scholar 

  291. A. Ralston and P. Rabinowitz, A First Course in Numerical Analysis, McGraw-Hill, New York, 2nd ed., 1978.

    Google Scholar 

  292. S. Ranjit, Risk management of currency portfolios, master’s thesis, Marquette University Department of Economics, Milwaukee, Wisc., April 1998.

    Google Scholar 

  293. H. Ratschek, Die subdistributivität der intervallarithmetik, ZAMM, 54 (1971).

    Google Scholar 

  294. H. Ratschek and J. Rokne, Computer Methods for the Range of Functions, Ellis Horwood/Prentice-Hall, Chichester, 1984.

    Google Scholar 

  295. H. Ratschek and G. Schröder, Representation of semigroups as systems of compact convex sets, Proc. Amer. Math. Soc., 65 (1977), pp. 24–28.

    Article  MathSciNet  MATH  Google Scholar 

  296. D. Ratz, An inclusion algorithm for global optimization in a portable PASCAL-XSC implementation,in Computer Arithmetic and Enclosure Methods, L. Atanassova and J. Herzberger, eds., Amsterdam, 1992, North-Holland, pp. 329–338.

    Google Scholar 

  297. D. Ratz, Box-splitting strategies for the interval Gauss-Seidel step in a global optimization method, Computing, 53 (1994), pp. 337–354.

    Article  MathSciNet  MATH  Google Scholar 

  298. D. Ratz and T. Csendes, On the selection of subdivision directions in interval branch-andbound methods for global optimization, Journal of Global Optimization, 7 (1995), pp. 183–207.

    Article  MathSciNet  MATH  Google Scholar 

  299. P. L. Richman, Automatic error analysis for determining precision, Comm. ACM, 15 (1972), pp. 813–817.

    Article  MathSciNet  MATH  Google Scholar 

  300. R. Rihm, On a class of enclosure methods for initial value problems, Computing, 53 (1994), pp. 369–377.

    Article  MathSciNet  MATH  Google Scholar 

  301. J. Rohn, Systems of linear interval equations, Linear Algebra and Its Applications, 126 (1989), pp. 39–78.

    Article  MathSciNet  MATH  Google Scholar 

  302. J. Rohn, NP-hardness results for linear algebraic problems with interval data, in Topics in Vali- dated Computations: Proceedings of the IMACS-GAMM International Workshop on Validated Computations (Oldenburg, 30 Aug.–3 Sept., 1993), J. Herzberger, ed., Studies in Computational Mathematics, No. 5, Amsterdam, 1994, North-Holland/Elsevier, pp. 463–471.

    Google Scholar 

  303. J. Rohn, Positive definiteness and stability of interval matrices, SIAM J. Matrix Anal. Appl., 15 (1994), pp. 175–184.

    Article  MathSciNet  MATH  Google Scholar 

  304. M. Rueher and C. Solnon, Concurrent cooperating solvers within the reals, Reliable Computing, 3 (1997), pp. 325–333.

    Article  MATH  Google Scholar 

  305. S. M. Rump, Kleine Fehlerschranken bei Matrixproblemen, PhD thesis, Universität Karlsruhe, 1980.

    MATH  Google Scholar 

  306. S. M. Rump, Improved iteration schemes for the validation algorithms for dense and sparse nonlin- ear systems, Computing, 57 (1992), pp. 77–84.

    Article  MathSciNet  Google Scholar 

  307. S. M. Rum, On the solution of interval linear systems, Computing, 47 (1992), pp. 337–353.

    Article  MathSciNet  MATH  Google Scholar 

  308. S. M. Rum, Validated solution of large linear systems, in Computing Supplementum 9, Valida- tion Numerics, R. Albrecht, G. Alefeld, and H. J. Stetter, eds., Springer-Verlag, Berlin, 1993, pp. 191–212.

    Google Scholar 

  309. S. M. Rum, Verification methods for dense and sparse systems of equations, in Topics in Validated Computations: Proceedings of the IMACS-GAMM International Workshop on Validated Computations (Oldenburg, 30 Aug.–3 Sept., 1993), J. Herzberger, ed., Studies in Computational Mathematics, No. 5, North-Holland/Elsevier, Amsterdam, 1994, pp. 63–136.

    Google Scholar 

  310. S. M. Rum, Fast and parallel interval arithmetic, BIT, 39 (1999), pp. 539–560.

    Google Scholar 

  311. S. M. Rum, INTLAB–INTerval LABoratory, in Developments in Reliable Computing, T. Csendes, ed., Kluwer, Dordrecht, Netherlands, 1999, pp. 77–105.

    Google Scholar 

  312. Y. Saad, Iterative Methods for Sparse Linear Systems, PWS, Boston, 1996.

    MATH  Google Scholar 

  313. R. L. Sagula, Avaliacao de Desempenho de Bibliotecas Intervalares, PhD thesis, Porto Alegre; II da UFRGS, 1997.

    Google Scholar 

  314. R. L. Sagula, T. Diverio, and J. Netto, Performance evaluation technique STU and libavi library, in Developments in Reliable Computing, T. Csendes, ed., Kluwer, Dordrecht, Netherlands, 1999, pp. 131–140.

    Google Scholar 

  315. R. L. Sagula and T. A. Diverio, Interval software performance. Presented at the International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics, SCAN ‘87 (Lyon, France, Sept. 10–12, 1997 ), 1997.

    Google Scholar 

  316. D. Sarma and D. W. Matula, Faithful bipartite ROM reciprocal tables, in Proceedings of the 12th IEEE Symposium on Computer Arithmetic (Bath, UK, July 1995 ), S. Knowles and W. McAllister, eds., Los Alamitos, CA, 1995, IEEE Computer Society Press, pp. 17–28.

    Chapter  Google Scholar 

  317. Y. Sato, M. Hirata, T. Maruyama, and Y. Arita, Efficient collision detection using fast distance-calculation algorithms for convex and non-convex objects, in Proc. IEEE Intern. Conf. on Robotics and Automation (Minneapolis, Minnesota 1996), IEEE, 1996, pp. 771–778.

    Google Scholar 

  318. M. J. Schulte and J. Stine, Accurate function approximation by symmetric table lookup and addition, in Proceedings of ASAP ‘87, Los Alamitos, CA, 1997, IEEE Computer Society Press.

    Google Scholar 

  319. M. J. Schulte, Symmetric bipartite tables for accurate function approximation,in Proceedings of the 13th IEEE Symposium on Computer Arithmetic, T. Lang, J.-M. Muller, and N. Takagi, eds., Los Alamitos, CA, 1997, IEEE Computer Society Press, pp. 175–183.

    Google Scholar 

  320. M. J. Schulte and E. E. Swartzlander, JR., Variable-precision, interval arithmetic coprocessors, Reliable Computing, 2 (1996), pp. 47–62.

    Article  MATH  Google Scholar 

  321. M. J. Schulte, V. A. Zelov, A. Akkas, and J. C. Burley, The interval-enhanced GNU Fortran compiler, in Developments in Reliable Computing, T. Csendes, ed., Kluwer, Dordrecht, Netherlands, 1999, pp. 311–322. Also Reliable Computing 5/3 (1999), pp. 311–322.

    Google Scholar 

  322. M. J. Schulte, V. A. Zelov, G. W. Walster, and D. Chiriaev, Single-number interval I/O, in Developments in Reliable Computing, T. Csendes, ed., Kluwer, Dordrecht, Netherlands, 1999, pp. 141–148.

    Google Scholar 

  323. G. Schumacher, Genauigkeitsfragen bei algebraisch-numerischen Algorithmen auf Skalarund Vektorrechnern, PhD thesis, Universität Karlsruhe, 1989.

    Google Scholar 

  324. G. Schumacher, Computer aided numerical analysis, (to appear, 2000 ).

    Google Scholar 

  325. G. Schumacher and K. Musch, Specification of a test case generator for ranges of data, Deliverable T3/3/2 ESPRIT Project No. 23920, OMI/SAFE, 1998.

    Google Scholar 

  326. L. Schwartz, Theorie des distributions, I, Hermann, Paris, 1950.

    Google Scholar 

  327. E. Schwarz, High-Radix Algorithms for High-Order Arithmetic Operations, PhD thesis, Dept. of Electrical Engineering, Stanford University, 1992.

    Google Scholar 

  328. C. E. Shannon, The Mathematical Theory of Communication, University of Illinois Press, Urbana, 1949.

    MATH  Google Scholar 

  329. S. P. Shary, Solving the linear interval tolerance problem, Mathematics and Computers in Simulation, 39 (1995), pp. 53–85.

    Article  MathSciNet  Google Scholar 

  330. S. P. Shary, Algebraic approach to the interval linear static identification, tolerance and control problems, or one more application of Kaucher arithmetic, Reliable Computing, 2 (1996), pp. 3–33.

    Article  MathSciNet  MATH  Google Scholar 

  331. S. P. Shary, Algebraic solutions to interval linear equations and their applications, in Numerical Methods and Error Bounds, G. Alefeld and J. Herzberger, eds., Akademie Verlag, Berlin, 1996, pp. 224–233.

    Google Scholar 

  332. S. P. Shary, A new approach to the analysis of static systems under interval uncertainty, in Sci- entific Computing and Validated Numerics: Proceedings of the International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics–SCAN ‘85, G. Alefeld, A. Frommer, and B. Lang, eds., Akademie Verlag, Berlin, 1996, pp. 118–132.

    Google Scholar 

  333. S. P. Shary, Algebraic approach in the “outer problem” for interval linear equations, Reliable Computing, 3 (1997), pp. 103–135.

    Article  MathSciNet  MATH  Google Scholar 

  334. S. P. Shary, Algebraic approach to the analysis of linear static systems under interval uncertainty,Izvestiya Akademii Nauk. Control Theory and Systems, 3 (1997), pp. 51–61. In Russian.

    Google Scholar 

  335. S. P. Shary, Interval Gauss-Seidel method for generalized solution sets to interval linear systems, in MISC ‘89–Workshop on Applications of Interval Analysis to Systems and Control (Girona, Spain, February 24–26, 1999), Universidad de Girona, 1999, pp. 51–65.

    Google Scholar 

  336. S. P. Shary, Outer estimation of generalized solution sets to interval linear systems, in Develop- ments in Reliable Computing, T. Csendes, ed., Kluwer, Dordrecht, Netherlands, 1999, pp. 323–336. Also Reliable Computing 5/3 (1999), pp. 323–336.

    Google Scholar 

  337. M. A. Shayman, Geometry of the algebraic Riccati equation, part I and part II, SIAM J. Control and Optimization, 21 (1983), pp. 375–394, 395–409.

    Article  MathSciNet  Google Scholar 

  338. Siemens, Arithmos, Benutzerhandbuch, bibl.-nr. u 2900-i-z87–1, Siemens AG„ 1986.

    Google Scholar 

  339. V. Sima, Algorithms for Linear-Quadratic Optimization, Marcel Dekker, New York, 1996.

    MATH  Google Scholar 

  340. H. Simon, The Lcínczos Algorithm for Solving Symmetric Linear Systems, PhD thesis, University of California, Berkley, 1982.

    Google Scholar 

  341. S. Skelboe, Computation of rational functions, BIT, 14 (1974), pp. 87–95.

    Article  MathSciNet  MATH  Google Scholar 

  342. V. T. Sós, On the distribution mod 1 of the sequence na, Ann. Univ. Sci. Budapest, Eötvös Sect. Math., 1 (1958), pp. 127–134.

    MATH  Google Scholar 

  343. O. Spaniol, Die distributivität in der intervallarithmetik, Computing, 5 (1970).

    Google Scholar 

  344. O. Stauning, Automatic Validation of Numerical Solutions PhD thesis, Department of Mathematical Modelling, Technical University of Denmark, Lyngby, Denmark, October 1997. Also appeared at Technical Report IMM-PHD-1997–36.

    Google Scholar 

  345. Stevenson, D., Chairman, Floating-Point Working Group, Microprocessor Standards Subcommittee, IEEE standard for binary floating point arithmetic (IEEE/ANSI 754–1985), tech. report, IEEE, 1985.

    Google Scholar 

  346. J. E. Stine and M. J. Schulte, Hardware support for interval arithmetic, in Proceedings of 8th Great Lakes Symposium on VLSI, February 1998, pp. 208–213.

    Google Scholar 

  347. U. Storck, Verified calculation of the nodes and weights for Gaussian quadrature formulas, Interval Computations, 4 (1993), pp. 114–124.

    MathSciNet  Google Scholar 

  348. U. Storck, Verifizierte Berechnung mehrfach geschachtelter Integrale der Gaskinetik, PhD thesis, Universität Karlsruhe, 1995.

    MATH  Google Scholar 

  349. A. H. Stroud, Approximate Calculation of Multiple Integrals, Prentice-Hall, New York, 1971.

    MATH  Google Scholar 

  350. A. Strzebonski, An algorithm for systems of strong polynomial inequalities, The Mathematica Journal, 4 (1994), pp. 74–77.

    Google Scholar 

  351. A. Strzebonski, Computing in the field of complex algebraic numbers, J. Symbolic Comp., 24 (1997), pp. 647–656.

    Article  MathSciNet  MATH  Google Scholar 

  352. A. Strzebonski, A real polynomial decision algorithm using arbitrary-precision floating point arith- metic, in Developments in Reliable Computing, T. Csendes, ed., Kluwer, Dordrecht, Netherlands, 1999, pp. 337–346. Also Reliable Computing 5/3 (1999), pp. 337–346.

    Google Scholar 

  353. T. Sunaga, Geometry of numerals, master’s thesis, University of Tokyo, February 1956.

    Google Scholar 

  354. T. Sunaga, A basic theory of communication, Memoirs, 2 (1958), pp. 426–443.

    Google Scholar 

  355. T. Sunaga, Theory of an interval algebra and its application to numerical analysis, RAAG Mem- oirs, 2 (1958), pp. 29–46, 547–564.

    Google Scholar 

  356. T. Sunaga, Algebra of Analysis and Synthesis of Automata PhD thesis, University of Tokyo, Tokyo, February 1961. In Japanese.

    Google Scholar 

  357. T. Sunaga, Differential decreasing speed using small number of differences of teeth of gears Trans. of Japan Society of Mechanical Engineers, 39 (1973), pp. 3209–3216. In Japanese.

    Google Scholar 

  358. T. Sunaga, Design and Planning for Production Corona Publ., Tokyo, 1979. In Japanese.

    Google Scholar 

  359. J. Suranyi, Über die Anordnung der Vielfachen einer reellen Zahl mod 1, Ann. Univ. Sci. Budapest, Eötvös Sect. Math., 1 (1958), pp. 107–111.

    MathSciNet  MATH  Google Scholar 

  360. S. Swierczkowski, On successive settings of an arc on the circumference of a circle, Fundamenta Math., 46 (1958), pp. 187–189.

    MathSciNet  Google Scholar 

  361. T. Szulc, Rank of convex combinations of matrices, Reliable Computing, 2 (1996), pp. 181–185.

    Article  MathSciNet  MATH  Google Scholar 

  362. N. Takagi, T. Asada, and S. Yajima, Redundant CORDIC methods with a constant scale factor for sine and cosine computation, IEEE Transactions on Computers, 40 (1991), pp. 989–995.

    Article  MathSciNet  Google Scholar 

  363. G. Talenti, Best constant in Sobolev inequality, Ann. Math. Pure Appl., 110 (1976), pp. 353–372.

    Article  MathSciNet  MATH  Google Scholar 

  364. P. T. P. Tang, Table-driven implementation of the exponential function in IEEE floating-point arithmetic, ACM Trans. Math. Software, 15 (1989), pp. 144–157.

    Article  Google Scholar 

  365. P. T. P. Tang, Table-driven implementation of the logarithm function in IEEE floating-point arith- metic, ACM Trans. Math. Software, 16 (1990), pp. 378–400.

    Article  Google Scholar 

  366. P. T. P. Tang, Table lookup algorithms for elementary functions and their error analysis, in Proceed- ings of the 10th IEEE Symposium on Computer Arithmetic (Grenoble, France, June 1991 ), P. Kornerup and D. W. Matula, eds., Los Alamitos, CA, 1991, IEEE Computer Society Press, pp. 232–236.

    Google Scholar 

  367. P. T. P. Tang, Table-driven implementation of the expml function in IEEE floating-point arithmetic, ACM Trans. Math. Software, 18 (1992), pp. 211–222.

    Article  Google Scholar 

  368. P. J. Thalacker, K. Julien, P. G. Toumanoff, J. P. Daniels, G. F. Corliss, and R. B. Keap.Fott, Globsol case study: Portfolio management (Banc One), Technical Report, Department of Mathematics, Statistics and Computer Science, Marquette University, Milwaukee, Wisc., 1998.

    Google Scholar 

  369. M. Tienari, On the control of floating-point mantissa length in iterative computations, in Proceedings of the International Computing Symposium, A. Günter et al., ed., North Holland, 1974, pp. 315–322.

    Google Scholar 

  370. E. Tsang, Foundations of Constraint Satisfaction, Computation in Cognitive Science, Academic Press, 1993.

    Google Scholar 

  371. C. Ullrich, Scientific programming language concepts, ZAMM, 76 (1996), pp. 57–60.

    MATH  Google Scholar 

  372. P. Van Hentenryck, D. Mcallester, and D. Kapur, Solving polynomial systems using a branch and prune approach, SIAM Journal on Numerical Analysis, 34 (1997), pp. 797–827.

    Article  MathSciNet  MATH  Google Scholar 

  373. P. Van Hentenryck, L. Michel, and Y. Deville, Numerica: A Modeling Language for Global Optimization, MIT Press, Cambridge, Mass., 1997.

    Google Scholar 

  374. P. Van Hentenryck and J.-F. Puget, A constraint satisfaction approach to a circuit design problem, Journal of Global Optimization, 13 (1998), pp. 75–93.

    Article  MATH  Google Scholar 

  375. R. Van Iwaarden, An Improved Unconstrained Global Optimization Algorithm, PhD thesis, University of Colorado at Denver, Denver, Colorado, 1996.

    Google Scholar 

  376. R. Van Iwaarden, IADOL-C. Available from the author., 1997.

    Google Scholar 

  377. R. S. Varga, On higher order stable implicit methods for solving parabolic differential equations, J. Math. and Phys., 40 (1961), pp. 220–231.

    MathSciNet  MATH  Google Scholar 

  378. A. A. Vatolin, On linear programming problems with interval coefficients J. Comp. Mathem. and Math. Phys., 24 (1984), pp. 1629–1637. In Russian.

    Google Scholar 

  379. T. Veldhuizen, Expression templates, C++ Report, 7 (1995).

    Google Scholar 

  380. T. Veldhuizen and K. Ponnambalam, Linear algebra with C++ template metaprograms, Dr. Dobb’s Journal of Software Tools, 21 (1996), pp. 38–44.

    Google Scholar 

  381. J. E. Volder, The CORDIC computing technique, IRE Transactions on Electronic Computers, E.-8 (1959), pp. 330–334. Reprinted in Earl E. Swartzlander, Jr., Computer Arithmetic, vol 1, IEEE Computer Society Press, 1990, 14–17.

    Google Scholar 

  382. J. Von Neuman and H. H. Goldstine, Numerical inverting of matrices of high order, Bull. AMS, 53 (1947), pp. 1021–1099.

    Article  Google Scholar 

  383. G. W. Walster, M77 reference manual: Minnesota FORTRAN 1977 standards version Technical Report, University Computer Center, University of Minnesota, Minneapolis, Minn., 1983.

    Google Scholar 

  384. G. W. Walster, Philosophy and practicality of interval arithmetic, in Reliability in Computing: The Role of Interval Methods in Scientific Computing, R. E. Moore, ed., Academic Press, Boston, 1988, pp. 309–323.

    Google Scholar 

  385. G. W. Walster, Stimulating hardware and software support for interval arithmetic, in Applications of Interval Computations, R. B. Kearfott and V. Kreinovich, eds., Kluwer, Dordrecht, Netherlands, 1996, pp. 405–416.

    Chapter  Google Scholar 

  386. G. W. Walster, The extended real interval system.,April1998.

    Google Scholar 

  387. G. W. Walster and E. R. Hansen, Interval algebra, composite functions and dependence in compilers. Submitted to Reliable Computing. Available.

    Google Scholar 

  388. E. Walter and L. Pronzato, Identification of Parametric Models from Experimental Data, Communications and Control Engineering, Springer-Verlag, Berlin, 1997.

    Google Scholar 

  389. W. V. Walter, ACRITH-XSC: A Fortran-like language for verified scientific computing, in Scientific Computing with Automatic Result Verification, E. Adams and U. Kulisch, eds., Academic Press, Boston, 1993, pp. 45–70.

    Chapter  Google Scholar 

  390. J. S. Walther,A unified algorithm for elementary functions, in Proc. Spring Joint Computer Conf., 1971, pp. 379–385.

    Google Scholar 

  391. S. Wang, V. Piuri, and E. E. Swartzlander, JR., Hybrid CORDIC algorithms, IEEE Trans. on Computers, 46 (1997), pp. 1202–1207.

    Article  Google Scholar 

  392. Z. Wang, P. Tonellato, G. F. Corliss, and R. B. Kearfott, Globsol case study: Gene prediction (Genome Therapeutics), Technical Report, Department of Mathematics, Statistics and Computer Science, Marquette University, Milwaukee, Wisc., 1998.

    Google Scholar 

  393. G. Wanner, On the integration of stiff differential equations, Technical Report, Université de Genéve, Section de Mathematique, Geneva, October 1976.

    Google Scholar 

  394. G. Wanner, On the integration of stiff differential equations, in Proceedings of the Colloquium on Numerical Analysis, Internat. Ser. Numer. Math., No. 37, Basel, 1977, Birkhäuser, pp. 209–226.

    Google Scholar 

  395. M. Warmus, Calculus of approximations, Bull. Acad. Polon. Sci., Cl. III, IV (1956), pp. 253–259.

    Google Scholar 

  396. M. Warmus, Approximations and inequalities in the calculus of approximations. Classification of approximate numbers Bull. Acad. Polon. Sci., Ser. math. astr. et phys., IX (1961), pp. 241245.

    Google Scholar 

  397. Y. Watanabe and M. T. Nakao, Numerical verifications of solutions for nonlinear elliptic equations, Japan J. Indust. Appl. Math., 10 (1993), pp. 165–178.

    Article  MathSciNet  MATH  Google Scholar 

  398. Y. Watanabe, N. Yamamoto, and M. T. Nakao, A numerical verification method of solutions for the Navier-Stokes equations, in Developments in Reliable Computing, T. Csendes, ed., Kluwer, Dordrecht, Netherlands, 1999, pp. 347–358. Also Reliable Computing 5/3 (1999), pp. 347–358.

    Google Scholar 

  399. Waterloo Maple, Maple V Learning Guide, Springer-Verlag, Berlin, 1998.

    Google Scholar 

  400. K. Werner, Verifizierte Berechnung der inversen Weierstraß-Funktion und der elliptischen Funktion von Jacobi in beliebigen Maschinenarithmetiken, PhD thesis, Universität Duisburg, Duisburg, 1996.

    Google Scholar 

  401. J. C. Willems, Least squares stationary optimal control and the algebraic Riccati equation, IEEE Trans. Autom. Contr., 16 (1971), pp. 621–634.

    Article  Google Scholar 

  402. J. Wolff Von Gudenberg, Hardware support for interval arithmetic, in Scientific Computing and Validated Numerics: Proceedings of the International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics–SCAN 95, G. Alefeld, A. Frommer, and B. Lang, eds., Berlin, 1996, Akademie Verlag, pp. 32–37.

    Google Scholar 

  403. S. Wolfram, The Mathematica Book, Cambridge Univ. Press, Cambridge, 3rd. ed., 1996.

    Google Scholar 

  404. W. F. Wong and E. Goto, Fast hardware-based algorithms for elementary function computations using rectangular multipliers IEEE Transactions on Computers, 43 (1994), pp. 278294.

    Google Scholar 

  405. W. F. Wong, Fast evaluation of the elementary functions in single precision, IEEE Transactions on Computers, 44 (1995), pp. 453–457.

    Article  MATH  Google Scholar 

  406. A. G. Yakovlev, Multiaspectness and localization, Interval Computations, 4 (1993), pp. 195–209.

    Google Scholar 

  407. N. Yamamoto, A numerical verification method for solutions of boundary value problems with local uniqueness by Banach’s fixed-point theorem, SIAM J. Numer. Anal., 35 (1998), pp. 2004–2013.

    Article  MATH  Google Scholar 

  408. W. Yang and G. Corliss, Bibliography of computational differentiation, in Computational Differentiation: Techniques, Applications, and Tools, M. Berz, C. H. Bischof, G. F. Corliss, and A. Griewank, eds., SIAM, Philadelphia, Penn., 1996, pp. 393–418.

    Google Scholar 

  409. R. Young, The algebra of many-valued quantities, Math. Annalen, 104 (1932), pp. 260–290.

    Article  Google Scholar 

  410. V. A. Zelov and M. J. Schulte, Implementing and testing interval I/O in the GNU Fortran compiler, Technical Report, Lehigh University, December 1997.

    Google Scholar 

  411. V. A. Zelov, G. W. Walster, D. Chiriaev, and M. J. Schulte, Java(TM) programming environment for accurate numerical computing. presented at the International Workshop on Modern Software Tools for Scientific Computing, Oslo, Norway, September 1998.

    Google Scholar 

  412. J. Zemke, b4m - BIAS for Matlab, Technical Report, Inst. f. Informatik III, Technische Universität Hamburg-Harburg, 1998.

    Google Scholar 

  413. G. M. Ziegler, Lectures on Polytopes, Graduate Texts in Mathematics, No. 152, Springer-Verlag, Berlin, 1995.

    Google Scholar 

  414. R. Zurmühl and S. Falk, Matrizen und ihre Anwendungen, Springer-Verlag, Berlin, 1984.

    MATH  Google Scholar 

  415. V. S. Zyuzin, On a way of representation of the interval numbers. Presented at SCAN ‘88 (Budapest, Sept. 22–25, 1998 ), 1998.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Statistics, and Computer Science, Marquette University, P.O. Box 1881, Milwaukee, WI, 53201-1881, USA

    George F. Corliss

Authors
  1. George F. Corliss
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. József Attila University, Szeged, Hungary

    Tibor Csendes

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Corliss, G.F. (1999). SCAN-98 Collected Bibliography. In: Csendes, T. (eds) Developments in Reliable Computing. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1247-7_31

Download citation

  • DOI: https://doi.org/10.1007/978-94-017-1247-7_31

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5350-3

  • Online ISBN: 978-94-017-1247-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation