The Solution of Tridiagonal Linear Systems on the CDC STAR 100 Computer

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The Solution of Tridiagonal Linear Systems on the CDC STAR 100 Computer

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

Pages: 308 - 329

Year of Publication: 1975

ISSN:0098-3500

Authors

Jules J. Lambiotte, Jr.	NASA Langley Research Center, Hampton, VA
Robert G. Voigt	Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 8, Downloads (12 Months): 41, Citation Count: 13

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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	Control Data Corp. CDC STAR-100 Instruction Execution Times, Rev. 2, 1974.
	2	GOLUB, G. Private commumcation, 1974.
	3	HELLER, D. Some aspects of the cyclic reduction algorithm for block tndiagonal linear systems. ICASE Rep, NASA Langley Research Center, Hampton, Va., 1974.
	4	HELLER, D., STEVENSON, D, AND TRAUB, J Accelerated iterative methods for the solution of tridlagonal systems on parallel computers. Rep, Dep. Computer Sci., Carnegie-Mellon U., Pittsburgh, Pa, 1974.
	5	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]
	6	HOCKNEY, R.W. The potential calculation and some applications. Methods Computatwnal Phys. 9 (1970), 135-211.
	7	HOUSEHOLDER, A.S. The Theory of Matrices ~n Numerical Analyszs. Blaisdell, New York, 1964.
	8	SLOTNICK, D.L, BORCK, W.C, AND McREVNOLDS, R.C. The SOLOMON computer. In Proc. AFIPS 1962 Fall Joint Computer Conf, vol. 22, pp. 97-107.
	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	STONE, H.S. Parallel processing with the perfect shuffle. IEEE Trans. Computers C-20 (1971), 153-161.
	11	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]
	12	TR.~UB, J.F. Iterative solution of tridiagonal systems on parallel or vector computers. In Complexity of Sequential and Parallel Numemcal A lgomthms, J.F. Traub, Ed., Academic Press, New York, 1973, pp. 49-82.
	13	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]
	14	YOUNG, D.M. Iterative Solutwn of Large In'near Systems. Academic Press, New York, 1971.

CITED BY 13

	C. L. Cox, Implemention of a divide and conquer cyclic reduction algorithm on the FPS T-20 hypercube, Proceedings of the third conference on Hypercube concurrent computers and applications, p.1532-1538, January 1989, Pasadena, California, United States
	H. H. Wang, A Parallel Method for Tridiagonal Equations, ACM Transactions on Mathematical Software (TOMS), v.7 n.2, p.170-183, June 1981
	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
	L. Hyafil , H. T. Kung, The Complexity of Parallel Evaluation of Linear Recurrences, Journal of the ACM (JACM), v.24 n.3, p.513-521, July 1977
	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. 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
	T. Shirakawa , T. Hoshino , Y. Oyanagi , Y. Iwasaki , T. Yoshie, QCDPAX-an MIMD array of vector processors for the numerical simulation of quantum chromodynamics, Proceedings of the 1989 ACM/IEEE conference on Supercomputing, p.495-504, November 12-17, 1989, Reno, Nevada, United States
	Jacob T. Schwartz, Ultracomputers, ACM Transactions on Programming Languages and Systems (TOPLAS), v.2 n.4, p.484-521, Oct. 1980
	Harold S. Stone, Parallel Tridiagonal Equation Solvers, ACM Transactions on Mathematical Software (TOMS), v.1 n.4, p.289-307, Dec. 1975
	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
	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