A Parallel Method for Tridiagonal Equations

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A Parallel Method for Tridiagonal Equations

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 7 , Issue 2 (June 1981) table of contents

Pages: 170 - 183

Year of Publication: 1981

ISSN:0098-3500

Author

H. H. Wang

IBM Scientific Center, 1530 Page Mill Road, Palo Alto, CA

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 12, Downloads (12 Months): 81, Citation Count: 19

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references cited by index terms collaborative colleagues

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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	DUBOlS, P., AND RODRIGUE, G. An analysm of the recurslve doublmg algorithm. In Htgh Speed Computer and Algortthm Organtzation, D. J Kuck, D. H Lawne, and A. H Sameh, Eds., Academic Press, New York, 1977.
	2	EKLUNDH, J.O. A fast computer method for matrix transposing IEEE Trans. Comput. C-21 (1972), 801-803.
	3	GEORGE, A An efficient band-oriented scheme for solving nbyn grid problems. In Proc F1 Jt Computer Conf., AFIPS Press, Arlington, Va., 1972, pp. 1317-1320.
	4	Jules Joseph Lambiotte, Jr., The solution of linear systems of equations on a vector computer., 1975
	5	Jules J. Lambiotte, Jr. , Robert G. Voigt, The Solution of Tridiagonal Linear Systems on the CDC STAR 100 Computer, ACM Transactions on Mathematical Software (TOMS), v.1 n.4, p.308-329, Dec. 1975 [doi>10.1145/355656.355658]
	6	LORIN, H. Paralleltsm m Hardware and Software: Real and Apparent Concurrency. Prentice- Hall, Englewood Cliffs, N.J., 1972.
	7	SCHUMANN, U. Comments on "A fast computer method for matrix transposing" and application to the solution of Poisson's equation. IEEE Trans. Comput. C-22 (1973), 542-543.
	8	Harold S. Stone, Parallel Tridiagonal Equation Solvers, ACM Transactions on Mathematical Software (TOMS), v.1 n.4, p.289-307, Dec. 1975 [doi>10.1145/355656.355657]
	9	WACHSPRESS, E.L. interactwe Solution of Elliptic Systems. Prentice-Hall, Englewood Cliffs, N.J., 1966.
	10	WANG, H.H. Transposing matrices on a vector computer. Rep. G320-3389, IBM Palo Alto Scientific Center, Palo Alto, Calif., 1979.
	11	J. H. Wilkinson, Error Analysis of Direct Methods of Matrix Inversion, Journal of the ACM (JACM), v.8 n.3, p.281-330, July 1961 [doi>10.1145/321075.321076]

CITED BY 19

	Holger Bischof , Sergei Gorlatch, A cost-optimal parallel implementation of a tridiagonal system solver using skeletons, Future Generation Computer Systems, v.21 n.5, p.737-742, May 2005
	K. P. Traar , W. Mader , O. Heinreichsberger , S. Selberherr , M. Stiftinger, High performance preconditioning on supercomputers for the 3D device simulator MINIMOS, Proceedings of the 1990 conference on Supercomputing, p.224-231, October 1990, New York, New York, United States
	Xian-He Sun , Hong Zhang Sun , Lionel M. Ni, Parallel algorithms for solution of tridiagonal systems on multicomputers, Proceedings of the 3rd international conference on Supercomputing, p.303-312, June 05-09, 1989, Crete, Greece
	Pieter H. Hartel , Koen G. Langendoen, Benchmarking implementations of lazy functional languages, Proceedings of the conference on Functional programming languages and computer architecture, p.341-349, June 09-11, 1993, Copenhagen, Denmark
	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
	K. P. Traar , M. Stiftinger , O. Heinreichsberger , S. Selberherr, Three-dimensional simulation of semiconductor devices on supercomputers, Proceedings of the 5th international conference on Supercomputing, p.154-162, June 17-21, 1991, Cologne, West Germany
	Marcel Beemster, Strictness optimization for graph reduction machines (why id might not be strict), ACM Transactions on Programming Languages and Systems (TOPLAS), v.16 n.5, p.1449-1466, Sept. 1994
	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
	Zi-Niu Wu , Hui Zou, Efficient parallel method for implicit upwind schemes approximating the Euler equations in gas dynamics, Journal of Computational Physics, v.187 n.2, p.683-715, 20 May 2003
	Kuo-Liang Chung , Wen-Ming Yan , Jung-Gen Wu, Load-balanced parallel banded-system solvers, Theoretical Computer Science, v.289 n.1, p.313-334, 23 October 2002
	Xian-He Sun , Wu Zhang, A Parallel Two-Level Hybrid Method for Tridiagonal Systems and Its Application to Fast Poisson Solvers, IEEE Transactions on Parallel and Distributed Systems, v.15 n.2, p.97-106, February 2004
	Joan-Josep Climent , Leandro Tortosa , Antonio Zamora, A note on the recursive decoupling method for solving tridiagonal linear systems, Applied Mathematics and Computation, v.140 n.1, p.159-164, 30 July 2003
	Xian-He Sun , Hong Zhang , Lionel M. Ni, Efficient Tridiagonal Solvers on Multicomputers, IEEE Transactions on Computers, v.41 n.3, p.286-296, March 1992
	L. Dekker , E. Dekker, Parallel Minimal Norm Method for Tridiagonal Linear Systems, IEEE Transactions on Computers, v.44 n.7, p.942-946, July 1995
	J. Verkaik , H. X. Lin, A class of novel parallel algorithms for the solution of tridiagonal systems, Parallel Computing, v.31 n.6, p.563-587, June 2005
	Halis Sak , Süleyman Özekici , İlkay Boduroglu, Parallel computing in Asian option pricing, Parallel Computing, v.33 n.2, p.92-108, March, 2007
	H. X. Lin, Graph transformation and designing parallel sparse matrix algorithms beyond data dependence analysis, Scientific Programming, v.12 n.2, p.91-100, April 2004
	S. Chandra Sekhara Rao , Sarita, Parallel solution of large symmetric tridiagonal linear systems, Parallel Computing, v.34 n.3, p.177-197, March, 2008
	Chi-Ye Wu , Ting-Zhu Huang, Stability of block LU factorization for block tridiagonal matrices, Computers & Mathematics with Applications, v.57 n.3, p.339-347, February, 2009

INDEX TERMS

Primary Classification:
G. Mathematics of Computing

Additional Classification:
F. Theory of Computation
F.1 COMPUTATION BY ABSTRACT DEVICES
F.1.2 Modes of Computation
Subjects: Parallelism and concurrency

G. Mathematics of Computing
G.1 NUMERICAL ANALYSIS
G.1.3 Numerical Linear Algebra
Subjects: Linear systems (direct and iterative methods)

General Terms:
Theory

Collaborative Colleagues:

H. H. Wang: colleagues

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