Journal Article

A model for understanding numerical stability

Folkmar Bornemann

in IMA Journal of Numerical Analysis

Published on behalf of Institute of Mathematics and its Applications

Volume 27, issue 2, pages 219-231
Published in print April 2007 | ISSN: 0272-4979
Published online April 2007 | e-ISSN: 1464-3642 | DOI: http://dx.doi.org/10.1093/imanum/drl037
A model for understanding numerical stability

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We present a model of roundoff error analysis that combines simplicity with predictive power. Though not considering all sources of roundoff within an algorithm, the model is related to a recursive roundoff error analysis and therefore is capable of correctly predicting stability or instability of an algorithm. By means of nontrivial examples, such as the componentwise backward stability analysis of Gaussian elimination with a single iterative refinement step, we demonstrate that the model even yields quantitative backward error bounds that show all the known problem-dependent terms with the exception of dimension-dependent constants. The model can serve as a convenient tool for teaching or as a heuristic device to discover stability results before entering a further detailed analysis.

Keywords: numerical stability; model of roundoff error analysis; Gaussian elimination

Journal Article.  0 words. 

Subjects: Mathematics

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