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2006.404: A Survey of Componentwise Perturbation Theory

2006.404: Nicholas J. Higham (1994) A Survey of Componentwise Perturbation Theory. In: Walter Gautschi, (eds). 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 2000 > 15 Linear and multilinear algebra; matrix theory
MSC 2000 > 65 Numerical analysis
MIMS number:2006.404
Deposited By:Nick Higham
Deposited On:22 November 2006

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