Parallel Tridiagonal Equation Solvers

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Parallel Tridiagonal Equation Solvers

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 1 , Issue 4 (December 1975) table of contents

Pages: 289 - 307

Year of Publication: 1975

ISSN:0098-3500

Author

Harold S. Stone

Department of Electrical and Computer Engineering, University of Massachusetts, Amherst, Mass.

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 9, Downloads (12 Months): 92, Citation Count: 18

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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	BUZBEE, B.L., GObUB, G.H., AND ~IELSON, C.W. On direct methods for solving Poisson's equations. SIAM J. Numer. Anal. 7, 4 (Dec. 1970), 627-656.
	2	GAu~scHI, W. Computatlonul aspects of three-term recurrence re\|atlons. SIAM Rev. 9, (Jan. 1967), 24-82.
	3	GOLUB, G.H. Private commumcatmns, 1973.
	4	R. W. Hockney, A Fast Direct Solution of Poisson's Equation Using Fourier Analysis, Journal of the ACM (JACM), v.12 n.1, p.95-113, Jan. 1965 [doi>10.1145/321250.321259]
	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	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]
	7	TRAUB, J.F. iterative solution of tndiagonal systems on parallel or vector computers. In Complexity of Sequentzal and Parallel Numerical Algorithms, J.F. Traub, Ed. Academic Press, New York, 1973.

CITED BY 18

	S. Chandra Sekhara Rao , Sarita, Parallel solution of large symmetric tridiagonal linear systems, Parallel Computing, v.34 n.3, p.177-197, March, 2008
	C. Levit, Parallel solution of pentadiagonal systems using generalized odd-even elimination, Proceedings of the 1989 ACM/IEEE conference on Supercomputing, p.333-336, November 12-17, 1989, Reno, Nevada, United States
	S. Lakshmivarahan , Sudarshan K. Dhall, A new class of parallel algorithms for solving linear tridiagonal systems, Proceedings of 1986 ACM Fall joint computer conference, p.315-324, November 1986, Dallas, Texas, United States
	W. Morven Gentleman, Some Complexity Results for Matrix Computations on Parallel Processors, Journal of the ACM (JACM), v.25 n.1, p.112-115, Jan. 1978
	H. H. Wang, A Parallel Method for Tridiagonal Equations, ACM Transactions on Mathematical Software (TOMS), v.7 n.2, p.170-183, June 1981
	H. A. Presnell , R. P. Pargas, Communication along shortest paths in a tree machine, Proceedings of the 1981 conference on Functional programming languages and computer architecture, p.107-114, October 18-22, 1981, Portsmouth, New Hampshire, United States
	Garry H. Rodrigue , Niel K. Madsen , Jack I. Karush, Odd-Even Reduction for Banded Linear Equations, Journal of the ACM (JACM), v.26 n.1, p.72-81, Jan. 1979
	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
	D. E. Heller , D. K. Stevenson , J. F. Traub, Accelerated Iterative Methods for the Solution of Tridiagonal Systems on Parallel Computers, Journal of the ACM (JACM), v.23 n.4, p.636-654, Oct. 1976
	Jaime Seguel , Dorothy Bollman , John Feo, A Framework for the Design and Implementation of FFT Permutation Algorithms, IEEE Transactions on Parallel and Distributed Systems, v.11 n.7, p.625-635, July 2000
	Kuo-Liang Chung , Ferng-Ching Lin , Wen-Chin Chen, Cost-optimal parallel B-spline interpolations, ACM SIGARCH Computer Architecture News, v.18 n.3b, p.121-131, Sept. 1990
	O. Egecioglu , C. K. Koc , A. J. Laub, Prefix algorithms for tridiagonal systems on hypercube multiprocessors, Proceedings of the third conference on Hypercube concurrent computers and applications, p.1539-1545, January 1989, Pasadena, California, United States
	Siddhartha Chatterjee , Guy E. Blelloch , Marco Zagha, Scan primitives for vector computers, Proceedings of the 1990 ACM/IEEE conference on Supercomputing, p.666-675, November 12-16, 1990, New York, New York
	Siddhartha Chatterjee , Guy E. Blelloch , Marco Zagha, Scan primitives for vector computers, Proceedings of the 1990 conference on Supercomputing, p.666-675, October 1990, New York, New York, United States
	R. Barrio , B. Melendo , S. Serrano, On the numerical evaluation of linear recurrences, Journal of Computational and Applied Mathematics, v.150 n.1, p.71-86, January 2003
	Kuo-Liang Chung, Prefix Computations on a Generalized Mesh-Connected Computer with Multiple Buses, IEEE Transactions on Parallel and Distributed Systems, v.6 n.2, p.196-199, February 1995
	Michael T. Goodrich , Yossi Matias , Uzi Vishkin, Optimal parallel approximation for prefix sums and integer sorting, Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms, p.241-250, January 23-25, 1994, Arlington, Virginia, United States
	Jacob T. Schwartz, Ultracomputers, ACM Transactions on Programming Languages and Systems (TOPLAS), v.2 n.4, p.484-521, Oct. 1980