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The Contribution of T. Sunaga to Interval Analysis and Reliable Computing

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Developments in Reliable Computing

Abstract

The contribution of T. Sunaga to interval analysis and reliable computing is not well-known amongst specialists in the field. We present and comment Sunaga’s basic ideas and results related to the properties of intervals and their application.

The interval concept is on the borderline linking pure mathematics with reality and pure analysis with applied analysis.

T. Sunaga

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References

  1. G. Alefeld, J. Herzberger, Introduction to Interval Computations, Academic Press, New York, 1983.

    MATH  Google Scholar 

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

    Google Scholar 

  3. N. Dimitrova, S. 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. Kaucher, S. Markov, G. Mayer (Eds.), J. C. Baltzer Publ., IMACS, 12, 1991, 213–228.

    Google Scholar 

  4. N. Dimitrova, S. Markov, E. Popova, Extended interval arithmetics: new results and applications. In: Computer arithmetic and enclosure methods (Eds. L. Atanassova, J. Herzberger) North-Holland, Amsterdam, 1992, 225–232.

    Google Scholar 

  5. N. Dimitrova, S. Markov, A Validated Newton Type Method for Nonlinear Equations, Interval Computation, 1994, 2, 27–51.

    MathSciNet  Google Scholar 

  6. P. Henrici, Circular arithmetic and the determination of polynomial zeros. Springer Lecture Notes 228 (1971), 86–92.

    MathSciNet  Google Scholar 

  7. M. Iri, Guaranteed Accuracy and Fast Automatic Differentiation, KITE Journal of Electronics Engineering, Vol. 4., No. 1A, 34–40, 1993.

    Google Scholar 

  8. M. Iri, Automatic Differentiation, Special lecture, Bull. Jap. Soc. Industrial and Applied Mathematics, Vol. 3, 1, March, 1993.

    Google Scholar 

  9. M. Iri, The Role of Automatic Differentiation in Nonlinear Analysis and High-Quality Computation, TRISE 96–05, Technical report, Dept. of Information and System Engineering, Faculty of Science and Engineering, Chuo University, Tokyo, Japan, 1–12, 1996.

    Google Scholar 

  10. E. Kaucher, Algebraische Erweiterungen der Intervallrechnung unter Erhaltung der Ordnungsund Verbandstrukturen, Computing Suppl., 1 (1977), 65–79.

    Article  Google Scholar 

  11. E. Kaucher, Interval Analysis in the Extended Interval Space IR, Computing Suppl. 2, 33–49 (1980).

    Article  MathSciNet  Google Scholar 

  12. L. Kolev, Interval Methods for Circuit Analysis, World Scientific Publ., 1993.

    Google Scholar 

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

    MATH  Google Scholar 

  14. S. Markov, Some Applications of Extended Interval Arithmetic to Interval Iterations, Computing Suppl. 2, 1980, 69–84.

    Article  Google Scholar 

  15. S. Markov, Interval Differential Equations, Interval Mathematics 1980 (Ed. K. Nickel ), Acad. Press, 1981, 145–164.

    Google Scholar 

  16. S. Markov, On the Presentation of Ranges of Monotone Functions Using Interval Arithmetic; Interval Computations, No. 4 (6) (1992), 19–31.

    Google Scholar 

  17. S. Markov, On Directed Interval Arithmetic and its Applications, J. UCS, 1, 7 (1995), 510–521.

    Google Scholar 

  18. S. Markov, An Iterative Method for Algebraic Solution to Interval Equations, 1998, to appear in Applied Numerical Mathematics.

    Google Scholar 

  19. S. Markov, On the Algebraic Properties of Convex Bodies and Some Applications, submitted to J. Convex Analysis.

    Google Scholar 

  20. S. Markov, R. Alt, On the Relation Between Stochastic and Interval Arithmetic, preprint.

    Google Scholar 

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

    Article  MATH  Google Scholar 

  22. J. Norton, H. P: Lahanier, E. Walter (Eds.), Bounding Approaches to System Identification. Plenum Press, London, N. Y., 1996.

    Google Scholar 

  23. R. Moore, Interval Arithmetic and Automatic Error Analysis in Digital Computing, Applied Math. & Stat. Lab., Stanford University Technical Report No. 25 (1962); also: PhD Dissertation, Stanford University, October 1962.

    Google Scholar 

  24. R. Moore, Interval Analysis, Prentice-Hall, Englewood-Cliffs, N. J., 1966.

    MATH  Google Scholar 

  25. A. Neumaier, A Distributive Interval Arithmetic, Freiburger Intervall-Berichte 82/10, Inst. f. Angewandte Mathematik, U. Freiburg i. Br., 1982, 10, 31–38.

    Google Scholar 

  26. J. v. Neuman, H. H. Goldstine, Numerical Inverting of Matrices of High Order, Bull. AMS, 53, 11, 1947, 1021–1099.

    Article  Google Scholar 

  27. 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, 4, 489–496, 1986 (in Japanese).

    Google Scholar 

  28. K. Okumura, An Application of Interval Operations to Electric Network Analysis, Bull. of the Japan Society for Industrial and Applied Mathematics, 3, 2, 15–27, 1993 (in Japanese).

    Google Scholar 

  29. K. Okumura, Recent Topics of Circuit Analysis: an Application of Interval Arithmetic, J. of System Control Information Society of Japan, v. 40, 9, 393–400, 1996 (in Japanese).

    Google Scholar 

  30. M. Petrovich, Calculation with Numerical Intervals, Beograd, 1932 (in Serbian, Serbian title: Racunanje sa brojnim razmacima).

    Google Scholar 

  31. L. Pontrjagin, Topological Groups, Princeton Univ. Press, Princeton, 1946.

    Google Scholar 

  32. E. Popova, C. Ullrich, Embedding Directed Intervals in Mathematica. Revista de Informatica Teorica e Applicada, 3, 2, 1996, pp. 99–115.

    Google Scholar 

  33. H. Ratschek, G. Schroder, Representation of Semigroups as Systems of Compact Convex Sets, Proc. Amer. Math. Soc. 65 (1977), 24–28.

    Article  MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  36. T. Sunaga, Geometry of Numerals, Master Thesis, University of Tokio, February 1956.

    Google Scholar 

  37. T. Sunaga, A Basic Theory of Communication, Memoirs, 2, G-1 (1958), 426 113.

    Google Scholar 

  38. T. Sunaga, Theory of an Interval Algebra and its Application to Numerical Analysis, RAAG Memoirs, 2, Misc. II, 1958, 547–564.

    Google Scholar 

  39. T. Sunaga, Algebra of Analysis and Synthesis of Automata (in Japanese) Dr. thesis, University of Tokio, February 1961.

    Google Scholar 

  40. T. Sunaga, Differential Decreasing Speed Using Small Number of Differences of Teeths of Gear, Trans. of Japan Society of Mechanical Engineers, v. 39, No. 326, 1973, 3209–3216 (in Japanese).

    Article  Google Scholar 

  41. T. Sunaga, Design and Planning for Production, Corona Publ., Tokyo, 1979 (in Japanese).

    Google Scholar 

  42. M. Warmus, Calculus of Approximations, Bull. Acad. Polon. Sci., Cl. III, Vol. IV, No. 5 (1956), 253–259.

    MathSciNet  Google Scholar 

  43. M. Warmus, Approximations and Inequalities in the Calculus of Approximations. Classification of Approximate numbers, Bull. Acad. Polon. Sci., Ser. math. astr. et phys., vol. IX, No. 4, 1961, 241–245.

    MathSciNet  Google Scholar 

  44. R. Young, The Algebra of Many-valued Quantities, Math. Annalen, 104, 1932, 260–290.

    Article  Google Scholar 

  45. V. Zyuzin, On a Way of Representation of the Interval Numbers, SCAN-98 Conference materials ( Extended Abstracts ), Budapest 1998, 173–174.

    Google Scholar 

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Markov, S., Okumura, K. (1999). The Contribution of T. Sunaga to Interval Analysis and Reliable Computing. In: Csendes, T. (eds) Developments in Reliable Computing. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1247-7_14

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  • DOI: https://doi.org/10.1007/978-94-017-1247-7_14

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5350-3

  • Online ISBN: 978-94-017-1247-7

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