On Stable Parallel Linear System Solvers

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On Stable Parallel Linear System Solvers

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Journal of the ACM (JACM) archive
Volume 25 , Issue 1 (January 1978) table of contents

Pages: 81 - 91

Year of Publication: 1978

ISSN:0004-5411

Authors

A. H. Sameh	Department of Computer Science, University of Illinois, Urbana, IL
D. J. Kuck	Department of Computer Science, University of Illinois, Urbana, IL

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 10, Downloads (12 Months): 67, Citation Count: 21

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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	BANK, R E, AND ROSE, D J. Extrapolated fast d~rect algorithms for elhptlc boundary value problems In Algoruhms and Complextty, J F Traub, Ed, Academtc Press, New York, 1976
	2	CSANKY, L Fast parallel matrix inversion algorithms SIAM J Comptng 5 (1976), 618-623
	3	GILL, P E, Ex AL Methods for mo&fymg matrix factonzatlons Math Comput. 28 (1974), 505-535.
	4	HAMM~RLIN6, S A note on modifications to the Givens plane rotaUon J ln~ Math. Appl 13 (1974), 215-218.
	5	SAMEH, A , AND BRENT, R Solving triangular systems on a parallel computer To appear m SIAM J Numer Anal
	6	SAMEIJ, A , AND Kucr, D Linear system solvers for parallel computers Rep No UIUCDCS-R-75- 701, Dept of Comptr So , U of llhnols at Urbana-Champalgn, Urbana, IU , Dec 1974
	7	SAMFH, A , AND KtrcK, D A parallel QR algorithm for symmetric tndmgonal matrices. IEEE Trans Comptrs C-26 (1977), 147-153
	8	SCnWARZ, H R, RUTISHAUSER, H., AND STIE~EL, E Numerical Analysts of Symmetric Matrices Transl by P. Hertelendy, Prentice-Hail, Englewood Chffs, N J , 1973
	9	Harold S. Stone, An Efficient Parallel Algorithm for the Solution of a Tridiagonal Linear System of Equations, Journal of the ACM (JACM), v.20 n.1, p.27-38, Jan. 1973 [doi>10.1145/321738.321741]
	10	J. H. Wilkinson, The algebraic eigenvalue problem, Oxford University Press, Inc., New York, NY, 1988

CITED BY 21

	A. Pothen , P. Raghavan, Distributed orthogonal factorization, Proceedings of the third conference on Hypercube concurrent computers and applications, p.1610-1620, January 1989, Pasadena, California, United States
	Jacob T. Schwartz, Ultracomputers, ACM Transactions on Programming Languages and Systems (TOPLAS), v.2 n.4, p.484-521, Oct. 1980
	Michel Cosnard , El Mostafa Daoudi, Optimal algorithms for parallel Givens factorization on a coarse-grained PRAM, Journal of the ACM (JACM), v.41 n.2, p.399-421, March 1994
	R. E. Lord , J. S. Kowalik , S. P. Kumar, Solving Linear Algebraic Equations on an MIMD Computer, Journal of the ACM (JACM), v.30 n.1, p.103-117, Jan. 1983
	Mauro Leoncini , Giovanni Manzini , Luciano Margara, On the parallel complexity of matrix factorization algorithms, Proceedings of the ninth annual ACM symposium on Parallel algorithms and architectures, p.63-71, June 23-25, 1997, Newport, Rhode Island, United States
	M. Cosnard , Y. Robert, Complexity of parallel QR factorization, Journal of the ACM (JACM), v.33 n.4, p.712-723, Oct. 1986
	Josep-L. Larriba-Pey , Juan J. Navarro , Oriol Roig , Angel Jorba, A generalized vision of some parallel bidiagonal systems solvers, Proceedings of the 8th international conference on Supercomputing, p.404-411, July 11-15, 1994, Manchester, England
	S. Lennart Johnsson, Solving narrow banded systems on ensemble architectures, ACM Transactions on Mathematical Software (TOMS), v.11 n.3, p.271-288, Sept. 1985
	D H. Lawrie , A H. Sameh, The computation and communication complexity of a parallel banded system solver, ACM Transactions on Mathematical Software (TOMS), v.10 n.2, p.185-195, June 1984
	Erricos John Kontoghiorghes, Greedy givens algorithms for computing the rank-k updating of the QR decomposition, Parallel Computing, v.28 n.9, p.1257-1273, September 2002
	B. Louka, Givens elimination on systolic arrays, Proceedings of the 2nd international conference on Supercomputing, p.638-647, June 1988, St. Malo, France
	Vijay Balasubramanian , Prithviraj Banerjee, Tradeoffs in the Design of Efficient Algorithm-Based Error Detection Schemes for Hypercube Multiprocessors, IEEE Transactions on Software Engineering, v.16 n.2, p.183-196, February 1990
	Peter Arbenz , Andrew Cleary , Jack Dongarra , Markus Hegland, A comparison of parallel solvers for diagonally dominant and general narrow-banded linear systems, Parallel numerical linear algebra, Nova Science Publishers, Inc., Commack, NY, 2001
	M. D. Ercegovac , Tomas Lang, Redundant and On-Line CORDIC: Application to Matrix Triangularization and SVD, IEEE Transactions on Computers, v.39 n.6, p.725-740, June 1990
	Li-Xin Wang , Jerry M. Mendel, Three-Dimensional Structured Networks for Matrix Equation Solving, IEEE Transactions on Computers, v.40 n.12, p.1337-1346, December 1991
	Marc Hofmann , Erricos John Kontoghiorghes, Pipeline Givens sequences for computing the QR decomposition on a EREW PRAM, Parallel Computing, v.32 n.3, p.222-230, March 2006
	Eric Polizzi , Ahmed H. Sameh, A parallel hybrid banded system solver: the SPIKE algorithm, Parallel Computing, v.32 n.2, p.177-194, February 2006
	K.N. Balasubramanya Murthy , K. Bhuvaneswari , C. Siva Ram Murthy, A New Algorithm Based on Givens Rotations for Solving Linear Equations on Fault-Tolerant Mesh-Connected Processors, IEEE Transactions on Parallel and Distributed Systems, v.9 n.8, p.825-832, August 1998
	Andrew Kerr , Dan Campbell , Mark Richards, QR decomposition on GPUs, Proceedings of 2nd Workshop on General Purpose Processing on Graphics Processing Units, p.71-78, March 08-08, 2009, Washington, D.C.
	Alexander Tiskin, Communication-efficient parallel generic pairwise elimination, Future Generation Computer Systems, v.23 n.2, p.179-188, February 2007
	Maxim Naumov , Ahmed H. Sameh, A tearing-based hybrid parallel banded linear system solver, Journal of Computational and Applied Mathematics, v.226 n.2, p.306-318, April, 2009