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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Iterative refinement implies numerical stability for Gaussian elimination


Author: Robert D. Skeel
Journal: Math. Comp. 35 (1980), 817-832
MSC: Primary 65F05; Secondary 65F35
MathSciNet review: 572859
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Abstract: Because of scaling problems, Gaussian elimination with pivoting is not always as accurate as one might reasonably expect. It is shown that even a single iteration of iterative refinement in single precision is enough to make Gaussian elimination stable in a very strong sense. Also, it is shown that without iterative refinement row pivoting is inferior to column pivoting in situations where the norm of the residual is important.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1980-0572859-4
PII: S 0025-5718(1980)0572859-4
Keywords: Iterative refinement, iterative improvement, numerical stability, Gaussian elimination, pivoting, backward error analysis, roundoff analysis
Article copyright: © Copyright 1980 American Mathematical Society