Normwise scaling of second order polynomial matrices

Hung Yuan Fan; Wen Wei Lin; Paul Van Dooren

doi:10.1137/S0895479803434914

Normwise scaling of second order polynomial matrices

Hung Yuan Fan^*, Wen Wei Lin, Paul Van Dooren

^*Corresponding author for this work

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

47 Citations (Scopus)

Abstract

We propose a minimax scaling procedure for second order polynomial matrices that aims to minimize the backward errors incurred in solving a particular linearized generalized eigenvalue problem. We give numerical examples to illustrate that it can significantly improve the backward errors of the computed eigenvalue-eigenvector pairs.

Original language	English
Pages (from-to)	252-256
Number of pages	5
Journal	SIAM Journal on Matrix Analysis and Applications
Volume	26
Issue number	1
DOIs	https://doi.org/10.1137/S0895479803434914
Publication status	Published - 2005
Externally published	Yes

Keywords

Balancing
Generalized eigenvalues
QZ algorithm

ASJC Scopus subject areas

Analysis

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10.1137/S0895479803434914

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title = "Normwise scaling of second order polynomial matrices",

abstract = "We propose a minimax scaling procedure for second order polynomial matrices that aims to minimize the backward errors incurred in solving a particular linearized generalized eigenvalue problem. We give numerical examples to illustrate that it can significantly improve the backward errors of the computed eigenvalue-eigenvector pairs.",

keywords = "Balancing, Generalized eigenvalues, QZ algorithm",

author = "Fan, {Hung Yuan} and Lin, {Wen Wei} and {Van Dooren}, Paul",

year = "2005",

doi = "10.1137/S0895479803434914",

language = "English",

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pages = "252--256",

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

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T1 - Normwise scaling of second order polynomial matrices

AU - Fan, Hung Yuan

AU - Lin, Wen Wei

AU - Van Dooren, Paul

PY - 2005

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AB - We propose a minimax scaling procedure for second order polynomial matrices that aims to minimize the backward errors incurred in solving a particular linearized generalized eigenvalue problem. We give numerical examples to illustrate that it can significantly improve the backward errors of the computed eigenvalue-eigenvector pairs.

KW - Balancing

KW - Generalized eigenvalues

KW - QZ algorithm

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DO - 10.1137/S0895479803434914

M3 - Article

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VL - 26

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EP - 256

JO - SIAM Journal on Matrix Analysis and Applications

JF - SIAM Journal on Matrix Analysis and Applications

IS - 1

ER -

Normwise scaling of second order polynomial matrices

Abstract

Keywords

ASJC Scopus subject areas

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