Structured backward error and condition of generalized eigenvalue problems

D.J. Higham; N.J. Higham

doi:10.1137/S0895479896313188

Structured backward error and condition of generalized eigenvalue problems

D.J. Higham, N.J. Higham

School of Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	493-512
Number of pages	20
Journal	SIAM Journal on Matrix Analysis and Applications
Volume	20
Issue number	2
DOIs	https://doi.org/10.1137/S0895479896313188
Publication status	Published - 1998

Keywords / Materials (for Non-textual outputs)

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

Access to Document

10.1137/S0895479896313188

Cite this

@article{182f07659b084899a78e4245220a75e0,

title = "Structured backward error and condition of generalized eigenvalue problems",

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.",

keywords = "generalized eigenvalue problem, quadratic eigenvalue problem, backward error, condition number, structured matrices, computer science, mathematics",

author = "D.J. Higham and N.J. Higham",

year = "1998",

doi = "10.1137/S0895479896313188",

language = "English",

volume = "20",

pages = "493--512",

journal = "SIAM Journal on Matrix Analysis and Applications",

issn = "0895-4798",

publisher = "Society for Industrial and Applied Mathematics Publications",

number = "2",

}

TY - JOUR

T1 - Structured backward error and condition of generalized eigenvalue problems

AU - Higham, D.J.

AU - Higham, N.J.

PY - 1998

Y1 - 1998

N2 - 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.

AB - 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.

KW - generalized eigenvalue problem

KW - quadratic eigenvalue problem

KW - backward error

KW - condition number

KW - structured matrices

KW - computer science

KW - mathematics

U2 - 10.1137/S0895479896313188

DO - 10.1137/S0895479896313188

M3 - Article

SN - 0895-4798

VL - 20

SP - 493

EP - 512

JO - SIAM Journal on Matrix Analysis and Applications

JF - SIAM Journal on Matrix Analysis and Applications

IS - 2

ER -

Structured backward error and condition of generalized eigenvalue problems

Abstract

Keywords / Materials (for Non-textual outputs)

Access to Document

Fingerprint

Cite this