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Mathematics of Computation

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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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Keywords: Iterative refinement, iterative improvement, numerical stability, Gaussian elimination, pivoting, backward error analysis, roundoff analysis
Article copyright: © Copyright 1980 American Mathematical Society

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