A sharp version of Bauer–Fike’s theorem

doi:10.1016/j.cam.2012.02.021

Journal of Computational and Applied Mathematics

Volume 236, Issue 13, July 2012, Pages 3218-3227

Dedicated to Prof. Zhi-hao Cao on the occasion of his 75th birthday

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Abstract

In this paper, we present a sharp version of Bauer–Fike’s theorem. We replace the matrix norm with its spectral radius or sign-complex spectral radius for diagonalizable matrices; 1-norm and $\infty$ -norm for non-diagonalizable matrices. We also give the applications to the pole placement problem and the singular system.

MSC

15A09

65F20

Keywords

Bauer–Fike’s theorem

Sign-real spectral radius

Sign-complex spectral radius

Diagonalizable

Regular matrix pair

Single-input pole placement