## 2006.164: Structured backward error and condition of generalized eigenvalue problems

2006.164:
Desmond J. Higham and Nicholas J. Higham
(1998)
*Structured backward error and condition of generalized eigenvalue problems.*
SIAM Journal On Matrix Analysis And Applications, 20 (2).
pp. 493-512.
ISSN 1095-7162

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DOI: 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.

Item Type: | Article |
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Uncontrolled Keywords: | generalized eigenvalue problem, quadratic eigenvalue problem, backward error, condition number, structured matrices |

Subjects: | MSC 2000 > 15 Linear and multilinear algebra; matrix theory MSC 2000 > 65 Numerical analysis |

MIMS number: | 2006.164 |

Deposited By: | Miss Louise Stait |

Deposited On: | 03 July 2006 |

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