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BIT Numerical Mathematics

, 48:493 | Cite as

Two perturbation bounds for singular values and eigenvalues

  • Xiao Shan Chen
Article
  • 86 Downloads

Abstract

The relative error in \(\hat{\alpha}=\alpha(1+\delta)\) as an approximation to α is measured by
$$\delta=\frac{\hat{\alpha}-\alpha}{\alpha}.$$
In terms of this measurement we give a Hoffman–Wielandt type bound of singular values under additive perturbations and a Bauer–Fike type bound of eigenvalues under multiplicative perturbations.

Key words

singular value eigenvalue perturbation bound Hoffman–Wielandt Bauer–Fike 

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Copyright information

© Springer Science + Business Media B.V. 2008

Authors and Affiliations

  1. 1.School of Mathematical SciencesSouth China Normal UniversityGuangzhouP.R. China

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