Structured backward error and condition of generalized eigenvalue problems

Higham, Desmond J. and Higham, Nicholas J. (1998) Structured backward error and condition of generalized eigenvalue problems. SIAM Journal On Matrix Analysis And Applications, 20 (2). pp. 493-512. ISSN 1095-7162

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Abstract

Backward errors and condition numbers are defined and evaluated for eigenvalues and eigenvectors of generalized eigenvalue problems. Both normwise and componentwise measures are used. Unstructured problems are considered first, and then the basic definitions are extended so that linear structure in the coefficient matrices (for example, Hermitian, Toeplitz, Hamiltonian, or band structure) is preserved by the perturbations.

Item Type: Article
Uncontrolled Keywords: generalized eigenvalue problem, quadratic eigenvalue problem, backward error, condition number, structured matrices
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: 03 Jul 2006
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/343

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