Scaling for Numerical Stability in Gaussian Elimination

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Scaling for Numerical Stability in Gaussian Elimination

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Journal of the ACM (JACM) archive
Volume 26 , Issue 3 (July 1979) table of contents

Pages: 494 - 526

Year of Publication: 1979

ISSN:0004-5411

Author

Robert D. Skeel

Department of Computer Science, 222 Digital Computer Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 13, Downloads (12 Months): 96, Citation Count: 6

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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	BAUER, F L On the definition of condition numbers and their relation to closed methods for solving linear systems lnformanon Processmg, Proc Int Conf Inform Processing, Unesco Paris, June 1959, Butterworth, London, 1960, pp 109-110
	2	BAUER, F L Optimally scaled matrices Numer Math 5 (1963), 78-87
	3	BAUER, F L Genamgkeitsfragen bel der Losung hnearer Gleichungssysteme ZAMM 46, 7 (Nov 1966), 409- 421
	4	BAUER, F L Computational graphs and rounding error SlAM J Numer Anal 11, I (Mar 1974), 87-96
	5	CURTIS, A R, AND REID, J K On the automatic scahng of mamces for Gausslan elimination J Inst Math Apphc 10, 1 (Aug 1972), 118-124
	6	FORSYTHE, G E, AND MOLER, C B Computer Solution of LmearAlgebralc Systems Prentice-Hall, Englewood Chffs, N J, 1967
	7	FORSYTHE, G E, AND STRAUS, E G On best conditioned matrices Proc Amer Math Soc 6 (1955), 340- 345
	8	GEAR, C W Numerical errors m sparse hnear equations File F-75-885, Dept Compt So, U of llhnols at Urbana-Champaign, Urbana, I11, May 1975
	9	Richard W. Hamming, Introduction to applied numerical analysis, Taylor & Francis/Hemisphere, Bristol, PA, 1989
	10	JANKOWSKI, M, AND WOZNIAKOWSKI, M lterattve refinement tmphes numerical stability BIT 17 (1977), 303-311
	11	KAHAN, W Numerical linear algebra Canad Math Bull 9 (1966), 757-801
	12	MILLER, W Automatic a priori round-off analysis, I Computing 10 (1972), 97-106
	13	MILLER, W On the stability of fimte numerical procedures Numer Math 19 (1972), 425-432
	14	Webb Miller, Computer Search for Numerical Instability, Journal of the ACM (JACM), v.22 n.4, p.512-521, Oct. 1975 [doi>10.1145/321906.321916]
	15	MILLER, W Roundoff analysis by direct comparison of two algorithms SIAM J Numer Anal 13, 3 (June 1976), 382-392
	16	MILLER. W Roundoff analyses and sparse data Numer Math 29, 1 (1977), 37-43
	17	OETTLI, W, AND PRAGER, W Compatibility of approximate solution of linear equations with given error bounds for coefficients and right-hand sides Numer Math 6 (1964), 405-409
	18	G. Peters , J. H. Wilkinson, On the stability of Gauss-Jordan elimination with pivoting, Communications of the ACM, v.18 n.1, p.20-24, Jan. 1975 [doi>10.1145/360569.360653]
	19	SHERMAN, A.H. Algorithms for sparse Gaussian elimination with partial pivoting Rep. R-76-817, Dept. Comput. Sci., U. of llhnois at Urbana-Champaign, Urbana, II1., July 1976
	20	SKEEL, R.D. Iterative refinement implies numerical stability for Gausslan ehmmation Manuscript, Dept. Comptr. Scl, U. of Illinois at Urbana-Champalgn, Urbana, Ill., July 1978 Submitted to a technical journal.
	21	STEWART, G W lntroductwn to Matrix Computations Academic Press, New York, 1973
	22	VAt~ PEg SLUIS, A Stability of solutions ofhnear algebraic systems Numer Math. 14 (1970), 246-251
	23	VAN DES SLUIS, A Condition, equilibration, and pivoting in linear algebraic systems Numer Math 15 (1970), 74-86
	24	James H. Wilkinson, Rounding Errors in Algebraic Processes, Dover Publications, Incorporated, 1994

CITED BY 6

	R. Barrio , J. M. Peña, Numerical evaluation of the pth derivative of Jacobi series, Applied Numerical Mathematics, v.43 n.4, p.335-357, December 2002
	Yang Cao , Linda Petzold, An error estimate for matrix equations, Applied Numerical Mathematics, v.50 n.3-4, p.395-407, September 2004
	Allan MacLeod, An instability problem in Chebyshev expansions for special functions, ACM SIGNUM Newsletter, v.28 n.2, p.2-7, April 1993
	Hua Xiang , Yimin Wei, Structured mixed and componentwise condition numbers of some structured matrices, Journal of Computational and Applied Mathematics, v.202 n.2, p.217-229, May, 2007
	Haiming Zhang , Hua Xiang , Yimin Wei, Condition numbers for linear systems and Kronecker product linear systems with multiple right-hand sides, International Journal of Computer Mathematics, v.84 n.12, p.1805-1817, December 2007
	Liangmin Zhou , Yiqin Lin , Yimin Wei , Sanzheng Qiao, Brief paper: Perturbation analysis and condition numbers of symmetric algebraic Riccati equations, Automatica (Journal of IFAC), v.45 n.4, p.1005-1011, April, 2009