On rank properties of Toeplitz matrices over finite fields

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On rank properties of Toeplitz matrices over finite fields

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International Conference on Symbolic and Algebraic Computation archive
Proceedings of the 1996 international symposium on Symbolic and algebraic computation table of contents

Zurich, Switzerland

Pages: 241 - 249

Year of Publication: 1996

ISBN:0-89791-796-0

Authors

E. Kaltofen	Department of Mathematics, North Carolina State University, Raleigh, North Carolina
A. Lobo	Department of Computer and Information Sciences, The University of Delaware, Newark, Delaware

Sponsors

SIGSAM: ACM Special Interest Group on Symbolic and Algebraic Manipulation
SIGNUM: ACM Special Interest Group on Numerical Mathematics

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 5, Downloads (12 Months): 30, Citation Count: 5

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REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	BORODIN, A., VON ZUR GATHEN, J., AND HOPCROFT, J. E. Fast parallel matrix and gcd computations. Inf. Control 52 (1982), 241-256.
	2	BRENT, R. P., GUSTAVSON, F. G., AND YUN, D. Y. Y. Fast solution of Toeplitz systems of equations and computation of Pad6 approximants. J. Algorithms 1 (1980), 259-295.
	3	W. S. Brown , J. F. Traub, On Euclid's Algorithm and the Theory of Subresultants, Journal of the ACM (JACM), v.18 n.4, p.505-514, Oct. 1971 [doi>10.1145/321662.321665]
	4	Don Coppersmith, Solving homogeneous linear equations over GF(2) via block Wiedemann algorithm, Mathematics of Computation, v.62 n.205, p.333-350, Jan. 1994 [doi>10.2307/2153413]
	5	DAYKIN, D. E. Distribution of bordered persymmetric matrices in a finite field. J. reine u. angew. Math. 203 (1960), 47-54.
	6	G ANTMACHER, F. R. The Theory of Matrices, Vol. 1. Chelsea Publ. Co., New York, N. Y., 1990.
	7	GOHBERG, I., KAILATH, T., AND KOLTRACHT, i. Elficient solution of linear systems of equations with recursive structure. Linear Algebra Applic. 80 (1986), 81-113.
	8	GaAGG, W. B. The Pad~ table and its relation to certain algorithms of numerical analysis. SIAM Review 1~, 1 (1972), 1-62.
	9	Erich Kaltofen, Analysis of Coppersmith's block Wiedemann algorithm for the parallel solution of sparse linear systems, Mathematics of Computation, v.64 n.210, p.777-806, April 1995 [doi>10.2307/2153451]
	10	Erich Kaltofen , B. David Saunders, On Wiedemann's Method of Solving Sparse Linear Systems, Proceedings of the 9th International Symposium, on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, p.29-38, October 07-11, 1991
	11	LANDSBERG, G. Uber eine anzahlbestimmung und eine damit zusammenh~ngende reihe. J. reine u. angew. Math. 111 (1893), 87-88.
	12	Austin Anthony Lobo, Matrix-free linear system solving and applications to symbolic computation, Rensselaer Polytechnic Institute, Troy, NY, 1996
	13	J. von zur Gathen , Keju Ma, Analysis of Euclidean algorithms for polynomials over finite fields, Journal of Symbolic Computation, v.9 n.4, p.429-455, April 1990 [doi>10.1016/S0747-7171(08)80021-1]
	14	D H Wiedemann, Solving sparse linear equations over finite fields, IEEE Transactions on Information Theory, v.32 n.1, p.54-62, Jan. 1986 [doi>10.1109/TIT.1986.1057137]

CITED BY 5

	Angel Díaz , Erich Kaltofen, FOXBOX: a system for manipulating symbolic objects in black box representation, Proceedings of the 1998 international symposium on Symbolic and algebraic computation, p.30-37, August 13-15, 1998, Rostock, Germany
	Erich Kaltofen , Wen-shin Lee , Austin A. Lobo, Early termination in Ben-Or/Tiwari sparse interpolation and a hybrid of Zippel's algorithm, Proceedings of the 2000 international symposium on Symbolic and algebraic computation, p.192-201, July 2000, St. Andrews, Scotland
	Erich Kaltofen , Wen-shin Lee, Early termination in sparse interpolation algorithms, Journal of Symbolic Computation, v.36 n.3-4, p.365-400, September 2003
	Jeffrey Adams , B. David Saunders , Zhendong Wan, Signature of symmetric rational matrices and the unitary dual of lie groups, Proceedings of the 2005 international symposium on Symbolic and algebraic computation, p.13-20, July 24-27, 2005, Beijing, China
	William J. Turner, Preconditioners for singular black box matrices, Proceedings of the 2005 international symposium on Symbolic and algebraic computation, p.332-339, July 24-27, 2005, Beijing, China