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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Official URL: http://dx.doi.org/10.1137/S0895479896313188

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.

Creators(s):	Higham, D.J. ORCID: https://orcid.org/0000-0002-6635-3461 and Higham, N.J.;
Item type:	Article
ID code:	184
Keywords:	generalized eigenvalue problem, quadratic eigenvalue problem, backward error, condition number, structured matrices, computer science, mathematics, Electronic computers. Computer science, Mathematics, Analysis
Subjects:	Science > Mathematics > Electronic computers. Computer science Science > Mathematics
Department:	Faculty of Science > Mathematics and Statistics
Depositing user:	Ms Sarah Scott
Date deposited:	02 Mar 2006
Last modified:	31 Jul 2020 00:48
URI:	https://strathprints.strath.ac.uk/id/eprint/184
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