A Survey of Componentwise Perturbation Theory

Higham, Nicholas J. (1994) A Survey of Componentwise Perturbation Theory. In: Mathematics of Computation 1943--1993: A Half Century of Computational Mathematics. Proceedings of Symposia in Applied Mathematics, 48 . American Mathematical Society, Providence, RI, USA, pp. 49-77. ISBN 0-8218-0291-7

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Abstract

Perturbation bounds in numerical linear algebra are traditionally derived and expressed using norms. Norm bounds cannot reflect the scaling or sparsity of a problem and its perturbation, and so can be unduly weak. If the problem data and its perturbation are measured componentwise, much smaller and more revealing bounds can be obtained. A survey is given of componentwise perturbation theory in numerical linear algebra, covering linear systems, the matrix inverse, matrix factorizations, the least squares problem, and the eigenvalue and singular value problems. Most of the results described have been published in the last five years.

Item Type: Book Section
Uncontrolled Keywords: componentwise perturbation bounds, componentwise backward error, linear systems, the matrix inverse, matrix factorizations, least squares problem, underdetermined system, eigenvalue problem, singular value problem.
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory
MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: Nick Higham
Date Deposited: 22 Nov 2006
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/651

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