Title

Sensitivity and computation of a defective eigenvalue

Document Type

Article

Publication Date

1-1-2016

Abstract

A defective eigenvalue is well documented to be hypersensitive to data perturbations and round-oif errors, making it a formidable challenge in numerical computation particularly when the matrix is known through approximate data. This paper establishes a finitely bounded sensitivity of a defective eigenvalue with respect to perturbations that preserve the geometric multiplicity and the smallest Jordan block size. Based on this perturbation theory, numerical computation of a defective eigenvalue is regularized as a well-posed least squares problem so that it can be accurately carried out using floating point arithmetic even if the matrix is perturbed.

DOI

10.1137/15M1016266

Publication Title

SIAM Journal on Matrix Analysis and Applications

Volume Number

37

Issue Number

2

First Page

798

Last Page

817

ISSN

08954798

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