A Chart of Backward Errors for Singly and Doubly Structured Eigenvalue Problems

Tisseur, Françoise (2003) A Chart of Backward Errors for Singly and Doubly Structured Eigenvalue Problems. SIAM Journal on Matrix Analysis and Applications, 24 (3). pp. 877-897. ISSN 1095-7162

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Abstract

We present a chart of structured backward errors for approximate eigenpairs of singly and doubly structured eigenvalue problems. We aim to give, wherever possible, formulae that are inexpensive to compute so that they can be used routinely in practice. We identify a number of problems for which the structured backward error is within a factor $\sqrt{2}$ of the unstructured backward error. This paper collects, unifies, and extends existing work on this subject.

Item Type: Article
Uncontrolled Keywords: eigenvalue; backward error; condition number; eigenvector; symmetric matrix; Hermitian matrix; skew-symmetric matrix; skew-Hermitian matrix; symplectic matrix; conjugate symplectic matrix; Hamiltonian matrix
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory
MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: Ms Lucy van Russelt
Date Deposited: 04 Dec 2007
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/978

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