A sharp version of Bauer-Fike's theorem

Authors:
Xinghua Shi;Yimin Wei
Affiliations:
Institute of Mathematics, School of Mathematical Sciences, Fudan University, Shanghai, 200433, PR China;School of Mathematical Sciences, Fudan University, Shanghai, 200433, PR China and Shanghai Key Laboratory of Contemporary Applied Mathematics, Fudan University, Shanghai, 200433, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2012

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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 ~-norm for non-diagonalizable matrices. We also give the applications to the pole placement problem and the singular system.