# 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

## 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 generalized eigenvalue problem, quadratic eigenvalue problem, backward error, condition number, structured matrices MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theoryMSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis Ms Lucy van Russelt 03 Jul 2006 20 Oct 2017 14:12 http://eprints.maths.manchester.ac.uk/id/eprint/343

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