The Algebraic Solution of Sparse Linear Systems via Minor Expansion

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The Algebraic Solution of Sparse Linear Systems via Minor Expansion

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 2 , Issue 1 (March 1976) table of contents

Pages: 31 - 49

Year of Publication: 1976

ISSN:0098-3500

Author

Martin L. Griss

201 North Physics Building, University of Utah, Salt Lake City, UT

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 2, Downloads (12 Months): 16, Citation Count: 7

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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	BAREISS, E.H. Sylvester's identity and multi-step integer-preserving Gaussian elimination. Math. Comput. 2P (1968), 565-578; LIPSON, J.D., Symbolic methods for the solution of linear equations with applications to flowgraphs. Proc. 1968 Summer Institute of Symbolic Computation, IBM Programming Lab. Rep. FSC 69-0312, 1969.
	2	W. S. Brown, On computing with factored rational expressions, ACM SIGSAM Bulletin, v.8 n.3, p.26-34, August 1974 [doi>10.1145/1086837.1086842]
	3	GENTLEMAN, W.M. On the evaluation of symbolic determinants. U. of Waterloo, Waterloo, Ont., Canada, preprint 1972.
	4	W. M. Gentleman , S. C. Johnson, Analysis of algorithms, a case study: Determinants of polynomials, Proceedings of the fifth annual ACM symposium on Theory of computing, p.135-141, April 30-May 02, 1973, Austin, Texas, United States [doi>10.1145/800125.804044]
	5	Martin L. Griss, The algebraic solution of large sparse systems of linear equations using REDUCE 2, Proceedings of the 1974 annual conference, p.105-111, January 1974 [doi>10.1145/800182.810388]
	6	Anthony C. Hearn, REDUCE 2: A system and language for algebraic manipulation, Proceedings of the second ACM symposium on Symbolic and algebraic manipulation, p.128-133, March 23-25, 1971, Los Angeles, California, United States [doi>10.1145/800204.806277]
	7	E. Horowitz , S. Sahni, On Computing the Exact Determinant of Matrices with Polynomial Entries, Journal of the ACM (JACM), v.22 n.1, p.38-50, Jan. 1975 [doi>10.1145/321864.321868]
	8	Donald E. Knuth, The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms, Addison-Wesley Longman Publishing Co., Inc., Boston, MA, 1997
	9	SHTOKHAMER, R. Private communication, Computational Physics Group, U. of Utah, Salt Lake City.
	10	TwWARSON, R.P., Sparse matrices. Vol. 99 of Mathematics in Science and Engineering, Academic Press, New York, 1973.
	11	WOLFE, P., AND CROWDER, H. The substitution inverse of sparse matrices. IBM Watson Math. Sci. Dep., New York, preprint, 1972.

CITED BY 7

	Michael T. McClellan, A Comparison of Algorithms for the Exact Solution of Linear Equations, ACM Transactions on Mathematical Software (TOMS), v.3 n.2, p.147-158, June 1977
	Martin L. Griss, An efficient sparse minor expansion algorithm, Proceedings of the annual conference, p.429-434, October 20-22, 1976, Houston, Texas, United States
	S. Cabay , T. P. L. Lam, Congruence Techniques for the Exact Solution of Integer Systems of Linear Equations, ACM Transactions on Mathematical Software (TOMS), v.3 n.4, p.386-397, Dec. 1977
	Tateaki Sasaki , Yasumasa Kanada, Parallelism in algebraic computation and parallel algorithms for symbolic linear systems, Proceedings of the fourth ACM symposium on Symbolic and algebraic computation, p.160-167, August 05-07, 1981, Snowbird, Utah, United States
	Paul S. Wang , Tadatoshi Minamikawa, Taking advantage of zero entries in the exact inverse of sparse matrices, Proceedings of the third ACM symposium on Symbolic and algebraic computation, p.346-350, August 10-12, 1976, Yorktown Heights, New York, United States
	Stanley Cabay , Bart Domzy, Systems of linear equations with dense univariate polynomial coefficients, Journal of the ACM (JACM), v.34 n.3, p.646-660, July 1987
	David-Olivier Azulay , Ian Gambini, Which pivot to solve linear systems?, Journal of Computational and Applied Mathematics, v.147 n.2, p.471-484, October 2002