On randomized Lanczos algorithms

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On randomized Lanczos algorithms

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International Conference on Symbolic and Algebraic Computation archive
Proceedings of the 1997 international symposium on Symbolic and algebraic computation table of contents

Kihei, Maui, Hawaii, United States

Pages: 176 - 183

Year of Publication: 1997

ISBN:0-89791-875-4

Authors

Wayne Eberly	Department of Computer Science, University of Calgary, Calgary, Alberta, Canada T2N 1N4
Erich Kaltofen	Department of Mathematics, North Carolina State University, Raleigh, North Carolina

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

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Downloads (6 Weeks): 4, Downloads (12 Months): 24, Citation Count: 9

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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	COPPERSMITH, D. Solving linear equations over GF(2); block Lanczos algorithm. Linear Algebra Appl. 19~ (1993), 33-60.
	2	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]
	3	GRIgWANK, A. Achieving logarithmic growth of temporal and spatial complexity in reverse automatic differentiation. Optimization Methods ~4 Software 1 (1992), 35-54.
	4	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]
	5	Erich Kaltofen , Victor Pan, Processor efficient parallel solution of linear systems over an abstract field, Proceedings of the third annual ACM symposium on Parallel algorithms and architectures, p.180-191, July 21-24, 1991, Hilton Head, South Carolina, United States [doi>10.1145/113379.113396]
	6	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
	7	Brian A. LaMacchia , Andrew M. Odlyzko, Solving Large Sparse Linear Systems over Finite Fields, Proceedings of the 10th Annual International Cryptology Conference on Advances in Cryptology, p.109-133, August 11-15, 1990
	8	Robert John Lambert , Ian F. Blake, Computational aspects of discrete logarithms, 1996
	9	LANCZOS, C. Solution of systems of linear equations by minimized iterations. J. Res. Nat. Bureau of Standards 49 (1952), 33-53.
	10	MONT(;OMERV, P. L. A block Lanczos algorithm for finding dependencies over GF(2). In Proc. EURO- CRYPT '95 (Heidelberg, Germany, 1995), vol. 921 of Springer Lecture Notes Comput. Sci., Springer Verlag, pp. 106 120.
	11	PENFIELD JR., P., SPENCER, R., AND DUINKER, S. Tellegen's Theorem and Electrical Networks. M.I.T. Press, Cambridge, MA, 1970.
	12	J. T. Schwartz, Fast Probabilistic Algorithms for Verification of Polynomial Identities, Journal of the ACM (JACM), v.27 n.4, p.701-717, Oct. 1980 [doi>10.1145/322217.322225]
	13	TEITELBAUM, J. Euclid's algorithm and the Lanczos method over finite fields. Manuscript, January 1996.
	14	G. Villard, Further analysis of Coppersmith's block Wiedemann algorithm for the solution of sparse linear systems (extended abstract), Proceedings of the 1997 international symposium on Symbolic and algebraic computation, p.32-39, July 21-23, 1997, Kihei, Maui, Hawaii, United States [doi>10.1145/258726.258742]
	15	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]
	16	Richard Zippel, Probabilistic algorithms for sparse polynomials, Proceedings of the International Symposiumon on Symbolic and Algebraic Computation, p.216-226, June 01, 1979

CITED BY 9

	M. Giesbrecht , A. Lobo , B. D. Saunders, Certifying inconsistency of sparse linear systems, Proceedings of the 1998 international symposium on Symbolic and algebraic computation, p.113-119, August 13-15, 1998, Rostock, Germany
	G. Villard, Further analysis of Coppersmith's block Wiedemann algorithm for the solution of sparse linear systems (extended abstract), Proceedings of the 1997 international symposium on Symbolic and algebraic computation, p.32-39, July 21-23, 1997, Kihei, Maui, Hawaii, United States
	Jean-Guillaume Dumas , B. David Saunders , Gilles Villard, Integer Smith form via the valence: experience with large sparse matrices from homology, Proceedings of the 2000 international symposium on Symbolic and algebraic computation, p.95-105, July 2000, St. Andrews, Scotland
	Johannes Grabmeier , Erich Kaltofen , Volker Weispfenning, Cited References, Computer algebra handbook, Springer-Verlag New York, Inc., New York, NY, 2003
	B. D. Saunders, Black box methods for least squares problems, Proceedings of the 2001 international symposium on Symbolic and algebraic computation, p.297-302, July 2001, London, Ontario, Canada
	Wayne Eberly, Reliable Krylov-based algorithms for matrix null space and rank, Proceedings of the 2004 international symposium on Symbolic and algebraic computation, p.127-134, July 04-07, 2004, Santander, Spain
	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
	Wayne Eberly , Mark Giesbrecht , Pascal Giorgi , Arne Storjohann , Gilles Villard, Solving sparse rational linear systems, Proceedings of the 2006 international symposium on Symbolic and algebraic computation, July 09-12, 2006, Genoa, Italy
	Gilles Villard, Some recent progress in exact linear algebra and related questions, Proceedings of the 2007 international symposium on Symbolic and algebraic computation, July 29-August 01, 2007, Waterloo, Ontario, Canada