Structured backward error and condition of generalized eigenvalue problems

D.J. Higham, N.J. Higham

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

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 pages20
JournalSIAM Journal on Matrix Analysis and Applications
Issue number2
Publication statusPublished - 1998

Keywords / Materials (for Non-textual outputs)

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


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