Structured backward error and condition of generalized eigenvalue problems

D.J. Higham, N.J. Higham

Research output: Contribution to journalArticle

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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.
Original languageEnglish
Pages (from-to)493-512
Number of pages19
JournalSIAM Journal on Matrix Analysis and Applications
Volume20
Issue number2
DOIs
Publication statusPublished - 1998

Keywords

  • generalized eigenvalue problem
  • quadratic eigenvalue problem
  • backward error
  • condition number
  • structured matrices
  • computer science
  • mathematics

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