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

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.

ORCID iDs

Higham, D.J. ORCID: https://orcid.org/0000-0002-6635-3461

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  Item type:	Article
  ID code:	184
  Dates:	Date Event 1998 Published
  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:	02 Jul 2021 02:46
  URI:	https://strathprints.strath.ac.uk/id/eprint/184