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 | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0025-5718-1980-0572859-4

Keywords:
Iterative refinement,
iterative improvement,
numerical stability,
Gaussian elimination,
pivoting,
backward error analysis,
roundoff analysis

Article copyright:
© Copyright 1980
American Mathematical Society