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Relative perturbation results for matrix eigenvalues and singular values

Published online by Cambridge University Press:  07 November 2008

Ilse C. F. Ipsen
Affiliation:
Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, USA E-mail: ipsen@math.ncsu.eduhttp://www4.ncsu.edu/~ipsen/info.html

Abstract

It used to be good enough to bound absolute of matrix eigenvalues and singular values. Not any more. Now it is fashionable to bound relative errors. We present a collection of relative perturbation results which have emerged during the past ten years.

No need to throw away all those absolute error bound, though. Deep down, the derivation of many relative bounds can be based on absolute bounds. This means that relative bounds are not always better. They may just be better sometimes – and exactly when depends on the perturbation.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1998

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