This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
S. Berkowitz, On Computing the Determinant in Small Parallel Time Using a Small Number of Processors, Information Processing Letters, 18,3 1984, 147–150.
D. Bini, L. Gemignani, On the Euclidean Scheme for Polynomials, Proc. 2nd Ann. ACM SPAA 1990.
D. Bini, L. Gemignani, Fast Parallel Computations of the Polynomial Remainder Sequence via Bezout and Hankel Matrices, Dipartimento di Matematica Università di Pisa 1990.
A. Borodin and I. Munro, The Computational Complexity of Algebraic and Numeric Problems. American Elsevier, New York, 1975.
D. Bini, V. Pan, Numeric and Algebraic Computations with Matrices and Polynomials, Volume 1: Fundamental algorithms, Birkhäuser, Boston, 1991.
A.L. Chistov, Fast Parallel Calculation of the Rank of Matrices over a Field of Arbitrary Characteristics, Proc. FCT 85, Springer Lecture Notes in Computer Science, 199, 63–69, 1985.
J. Chun, T. Kailath and H. Lev-Ari, Fast Parallel Algorithm for QR-factorization of Structured Matrices, SIAM J. on Scientific and Statistical Computing, 8,6 899–913, 1987.
D. Eppstein and Z. Galil, Parallel Algorithmic Techniques for Combinatorial Computation, Annual Review of Computer Science 3 233–283, 1988.
M. Fiedler, Hankel and Loewner Matrices, Linear Algebra Appl. 58, 1984.
W. B. Gragg, A. Lindquist, On the Partial Realization Problem, Linear Algebra Appl., 50, 277–319, 1983.
U. Helmke, P.A. Fuhrmann Bezoutians, Linear Algebra Appl., 124, 1039–1097, 1989.
G. Heining, K. Rost, Algebraic Methods for Toeplitz-like Matrices and Operators, Operator Theory 13, Birkhauser 1984.
E. Kaltofen, Processor-Efficient Parallel Computation of Polynomial Greatest Common Divisor, PreliminaryReport, Dept. of Computer Sci., RPI, Troy, NY 1989.
E. Kaltofen and M. Singer, Size Efficient Parallel Algebraic Circuits for Partial Derivatives, Tech. Report 90-32, Computer Science Department, RPI Troy, NY 1990.
E. Kaltofen and V. Pan, Processor Efficient Parallel Solution of Linear Systems over an Abstract Field, Preliminary Report, 1991.
T. Kailath, S.-Y. Kung and M. Morf, Displacement Ranks of Matrices and Linear Equations, J. Math. Anal. Appl. 68,2 395–407 1979.
R. Karp and V. Ramachandran, Survey of Parallel Algorithms for Shared Memory Machines. Handbook of Theoretical Computer Science, North-Holland, Amsterdam, 869–941, 1990.
W. Keller-Gehrig, Fast Algorithms for the Characteristic Polynomial, Theor. Computer Sci. 36 309–317, 1985.
V. Pan, On Some Computations with Dense Structured Matrices, Proc. ACM-SIGSAM Intern. Symp. on Symbolic and Alg. Comp., 34–42, 1989 and Math. of Comp. 55, 191 179–190 1990.
V. Pan, Fast and Efficient Parallel Evaluation of the Zeros of a Polynomial Having Only Real Zeros, Computers and Math. (with Appl.) 17, 11, 1475–1481, 1989.
V. Pan, Parallel Least-Squares Solution of General and Toeplitz-like Linear Systems, Proc. 2nd Ann. ACM Symp. on Parallel Algorithms and Architecture 244–253 1990.
V. Pan, Parametrization of Newton's Iteration for Computations with Structured Matrices and Applications, report CUNY, CUCS-032-90, New York 1990, to appear in Computers and Math. (with Appl.), 1991.
A. Schönhage, The Fundamental Theorem of Algebra in Terms of Computational Complexity, manuscript, Dept. of Math., University of Tübingen Tübingen, West Germany 1982.
D.H. Wiedemann, Solving Sparse Linear Equations Over Finite Fields, IEEE Trans. on Inf. Theory IT-32,1 54–62 1986.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1991 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bini, D., Gemignani, L., Pan, V. (1991). Improved parallel computations with matrices and polynomials. In: Albert, J.L., Monien, B., Artalejo, M.R. (eds) Automata, Languages and Programming. ICALP 1991. Lecture Notes in Computer Science, vol 510. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54233-7_160
Download citation
DOI: https://doi.org/10.1007/3-540-54233-7_160
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-54233-9
Online ISBN: 978-3-540-47516-3
eBook Packages: Springer Book Archive