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# Structured backward error and condition of generalized eigenvalue problems

Higham, D.J. and Higham, N.J. (1998) Structured backward error and condition of generalized eigenvalue problems. SIAM Journal on Matrix Analysis and Applications, 20 (2). pp. 493-512. ISSN 0895-4798

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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 184 generalized eigenvalue problem, quadratic eigenvalue problem, backward error, condition number, structured matrices, computer science, mathematics, Electronic computers. Computer science, Mathematics, Analysis Science > Mathematics > Electronic computers. Computer scienceScience > Mathematics Faculty of Science > Mathematics and Statistics Ms Sarah Scott 02 Mar 2006 04 Sep 2014 10:01 http://strathprints.strath.ac.uk/id/eprint/184

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