Backward error, condition numbers, and pseudospectra for the multiparameter eigenvalue problem

M.E. Hochstenbach; Bor Plestenjak

doi:10.1016/S0024-3795(03)00613-X

Backward error, condition numbers, and pseudospectra for the multiparameter eigenvalue problem

M.E. Hochstenbach, Bor Plestenjak

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

21 Citations (Scopus)

Abstract

We define and evaluate the normwise backward error and condition numbers for the multiparameter eigenvalue problem (MEP). The pseudospectrum for the MEP is defined and characterized. We show that the distance from a right definite MEP to the closest non right definite MEP is related to the smallest unbounded pseudospectrum. Some numerical results are given.

Original language	English
Pages (from-to)	63-81
Journal	Linear Algebra and Its Applications
Volume	375
DOIs	https://doi.org/10.1016/S0024-3795(03)00613-X
Publication status	Published - 2003

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title = "Backward error, condition numbers, and pseudospectra for the multiparameter eigenvalue problem",

abstract = "We define and evaluate the normwise backward error and condition numbers for the multiparameter eigenvalue problem (MEP). The pseudospectrum for the MEP is defined and characterized. We show that the distance from a right definite MEP to the closest non right definite MEP is related to the smallest unbounded pseudospectrum. Some numerical results are given.",

author = "M.E. Hochstenbach and Bor Plestenjak",

year = "2003",

doi = "10.1016/S0024-3795(03)00613-X",

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T1 - Backward error, condition numbers, and pseudospectra for the multiparameter eigenvalue problem

AU - Hochstenbach, M.E.

AU - Plestenjak, Bor

PY - 2003

Y1 - 2003

N2 - We define and evaluate the normwise backward error and condition numbers for the multiparameter eigenvalue problem (MEP). The pseudospectrum for the MEP is defined and characterized. We show that the distance from a right definite MEP to the closest non right definite MEP is related to the smallest unbounded pseudospectrum. Some numerical results are given.

AB - We define and evaluate the normwise backward error and condition numbers for the multiparameter eigenvalue problem (MEP). The pseudospectrum for the MEP is defined and characterized. We show that the distance from a right definite MEP to the closest non right definite MEP is related to the smallest unbounded pseudospectrum. Some numerical results are given.

U2 - 10.1016/S0024-3795(03)00613-X

DO - 10.1016/S0024-3795(03)00613-X

M3 - Article

SN - 0024-3795

VL - 375

SP - 63

EP - 81

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Backward error, condition numbers, and pseudospectra for the multiparameter eigenvalue problem

Abstract

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