Processor efficient parallel solution of linear systems over an abstract field

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Processor efficient parallel solution of linear systems over an abstract field

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ACM Symposium on Parallel Algorithms and Architectures archive
Proceedings of the third annual ACM symposium on Parallel algorithms and architectures table of contents

Hilton Head, South Carolina, United States

Pages: 180 - 191

Year of Publication: 1991

ISBN:0-89791-438-4

Authors

Erich Kaltofen	Department of Computer Science, Rensselaer Polytechnic Institute, Troy, New York and Department of Computer Science, University of Toronto, Toronto, Canada M5S 1A4
Victor Pan	Department of Mathematics and Computer Science, Lehman College, City University of New York, Bronx, New York

Sponsors

SIGACT: ACM Special Interest Group on Algorithms and Computation Theory
SIGARCH: ACM Special Interest Group on Computer Architecture

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ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 4, Downloads (12 Months): 22, Citation Count: 29

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references cited by index terms collaborative colleagues peer to peer

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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.

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	2	Stuart J. Berkowitz, On computing the determinant in small parallel time using a small number of processors, Information Processing Letters, v.18 n.3, p.147-150, March 1984 [doi>10.1016/0020-0190(84)90018-8]
	3	Bini, D. and Pan, V., Numerical and Algebraic Computations with Matrices and Polynomials; Lecture Notes in Theor. Comput. Sci., edited by R. V. Book; Birkh~iuser Boston, Inc., 1991. To appear.
	4	Borodin, A., von zur Gathen, J., and ttopcrot't, J. E., "Fast parallel matrix and GCD computations," Inf. Control 52, pp. 241-256 (1982).
	5	Borodin, A. and Munro, I., Computational Complexity of Algebraic and Numeric Problems; American Elsevier, New York, N.Y., 1975.
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	7	Bunch, J. R. and Hopcroft, J. E., "Triangular factorization and inversion by fast matrix multiplication," Math. Comp. 28, pp. 231-236 (1974).
	8	David G. Cantor , Erich Kaltofen, On fast multiplication of polynomials over arbitrary algebras, Acta Informatica, v.28 n.7, p.693-701, Oct. 1991 [doi>10.1007/BF01178683]
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	11	Csanky, L., "Fast parallel matrix inversion algorithms," SIAM J. Comput. 5/4, pp. 618-623 (1976).
	12	Zvi Galil , Victor Pan, Parallel evaluation of the determinant and of the inverse of a matrix, Information Processing Letters, v.30 n.1, p.41-45, January 1989 [doi>10.1016/0020-0190(89)90173-7]
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	15	Michael Kaminski , David G. Kirkpatrick , Nader H. Bshouty, Addition requirements for matrix and transposed matrix products, Journal of Algorithms, v.9 n.3, p.354-364, September 1988 [doi>10.1016/0196-6774(88)90026-0]
	16	Richard M. Karp , Vijaya Ramachandran, Parallel algorithms for shared-memory machines, Handbook of theoretical computer science (vol. A): algorithms and complexity, MIT Press, Cambridge, MA, 1991
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	18	Lipson, J., Elements of Algebra and Algebraic Computing; Addison-Wesley Publ., Reading, Mass., 1981.
	19	V. Pan, Parallel least-squares solution of general and Toeplitz systems, Proceedings of the second annual ACM symposium on Parallel algorithms and architectures, p.244-253, July 02-06, 1990, Island of Crete, Greece [doi>10.1145/97444.97691]
	20	Pan, V., "Parameterization of Newton's iteration for computations with structured matrices and applications," Tech. Report CUCS-032-90, Comput. Sci. Dept., Columbia University, New York, N. Y., 1990b.
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	25	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 29

	Wayne Eberly , Erich Kaltofen, On randomized Lanczos algorithms, Proceedings of the 1997 international symposium on Symbolic and algebraic computation, p.176-183, July 21-23, 1997, Kihei, Maui, Hawaii, United States
	Victor Y. Pan, A new approach to parallel computation of polynomial GCD and to related parallel computations over fields and integer rings, Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms, p.518-527, January 28-30, 1996, Atlanta, Georgia, United States
	Wayne Eberly, Processor-efficient parallel matrix inversion over abstract fields: two extensions, Proceedings of the second international symposium on Parallel symbolic computation, p.38-45, July 20-22, 1997, Maui, Hawaii, United States
	Victor Y. Pan , Isdor Sobze , Antoine Atinkpahoun, Optimum parallel computations with banded matrices, Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms, p.649-658, January 23-25, 1994, Arlington, Virginia, United States
	John H. Reif, O(log2 n) time efficient parallel factorization of dense, sparse separable, and banded matrices, Proceedings of the sixth annual ACM symposium on Parallel algorithms and architectures, p.278-289, June 27-29, 1994, Cape May, New Jersey, United States
	Wayne Eberly, Early termination over small fields, Proceedings of the 2003 international symposium on Symbolic and algebraic computation, p.80-87, August 03-06, 2003, Philadelphia, PA, USA
	Wayne Eberly, Efficient parallel computations for singular band matrices, Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms, p.132-138, January 22-24, 1995, San Francisco, California, United States
	Joseph Cheriyan, A Las Vegas O(n2.38 algorithm for the cardinality of a maximum matching, Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms, p.442-451, January 23-25, 1994, Arlington, Virginia, United States
	Joseph Cheriyan , John H. Reif, Directed s-t numberings, rubber bands, and testing digraph k-vertex connectivity, Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms, p.335-344, September 1992, Orlando, Florida, United States
	Ioanis Z. Emiris , Victor Y. Pan, The structure of sparse resultant matrices, Proceedings of the 1997 international symposium on Symbolic and algebraic computation, p.189-196, July 21-23, 1997, Kihei, Maui, Hawaii, United States
	Piotr Sankowski, Processor efficient parallel matching, Proceedings of the seventeenth annual ACM symposium on Parallelism in algorithms and architectures, July 18-20, 2005, Las Vegas, Nevada, USA
	Victor Y. Pan , Xinmao Wang, Acceleration of Euclidean algorithm and extensions, Proceedings of the 2002 international symposium on Symbolic and algebraic computation, p.207-213, July 07-10, 2002, Lille, France
	William J. Turner, A block Wiedemann rank algorithm, Proceedings of the 2006 international symposium on Symbolic and algebraic computation, July 09-12, 2006, Genoa, Italy
	Xiaohan Huang , Victor Y. Pan, Fast rectangular matrix multiplications and improving parallel matrix computations, Proceedings of the second international symposium on Parallel symbolic computation, p.11-23, July 20-22, 1997, Maui, Hawaii, United States
	Victor Y. Pan , Franco P. Preparata, Supereffective slow-down of parallel computations, Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures, p.402-409, June 29-July 01, 1992, San Diego, California, United States
	Joseph Cheriyan , John H. Reif, Parallel and output sensitive algorithms for combinatorial and linear algebra problems, Proceedings of the fifth annual ACM symposium on Parallel algorithms and architectures, p.50-56, June 30-July 02, 1993, Velen, Germany
	Victor Y. Pan , Zhao Q. Chen, The complexity of the matrix eigenproblem, Proceedings of the thirty-first annual ACM symposium on Theory of computing, p.507-516, May 01-04, 1999, Atlanta, Georgia, United States
	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
	Erich Kaltofen, On computing determinants of matrices without divisions, Papers from the international symposium on Symbolic and algebraic computation, p.342-349, July 27-29, 1992, Berkeley, California, United States
	Erich Kaltofen, An output-sensitive variant of the baby steps/giant steps determinant algorithm, Proceedings of the 2002 international symposium on Symbolic and algebraic computation, p.138-144, July 07-10, 2002, Lille, France
	Erich Kaltofen , Victor Shoup, Subquadratic-time factoring of polynomials over finite fields, Proceedings of the twenty-seventh annual ACM symposium on Theory of computing, p.398-406, May 29-June 01, 1995, Las Vegas, Nevada, United States
	Ioannis Z. Emiris , Victor Y. Pan, Symbolic and numeric methods for exploiting structure in constructing resultant matrices, Journal of Symbolic Computation, v.33 n.4, p.393-413, April 2002
	G. Villard, Computing Popov and Hermite forms of polynomial matrices, Proceedings of the 1996 international symposium on Symbolic and algebraic computation, p.250-258, July 24-26, 1996, Zurich, Switzerland
	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
	Ioannis Z. Emiris , Victor Y. Pan, Improved algorithms for computing determinants and resultants, Journal of Complexity, v.21 n.1, p.43-71, February 2005
	John H. Reif, Work efficient parallel solution of Toeplitz systems and polynomial GCD, Proceedings of the twenty-seventh annual ACM symposium on Theory of computing, p.751-761, May 29-June 01, 1995, Las Vegas, Nevada, United States
	John H. Reif, Efficient parallel factorization and solution of structured and unstructured linear systems, Journal of Computer and System Sciences, v.71 n.1, p.86-143, July 2005
	Johannes Grabmeier , Erich Kaltofen , Volker Weispfenning, Cited References, Computer algebra handbook, Springer-Verlag New York, Inc., New York, NY, 2003
	Johannes Grabmeier , Erich Kaltofen , Volker Weispfenning, Cited References, Computer algebra handbook, Springer-Verlag New York, Inc., New York, NY, 2003