A Chart of Backward Errors for Singly and Doubly Structured Eigenvalue Problems

We present a chart of structured backward errors for approximate eigenpairs of singly and doubly structured eigenvalue problems. We aim to give, wherever possible, formulae that are inexpensive to compute so that they can be used routinely in practice. We identify a number of problems for which the...

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Bibliographic Details
Published inSIAM journal on matrix analysis and applications Vol. 24; no. 3; pp. 877 - 897
Main Author Tisseur, Françoise
Format Journal Article
LanguageEnglish
Published Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2003
Subjects
Algebra
Algorithms
Eigenvalues
Exact sciences and technology
Linear and multilinear algebra, matrix theory
Mathematics
Nonlinear algebraic and transcendental equations
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Ordinary differential equations
Sciences and techniques of general use
Error estimation
Symmetric matrix
Eigenvector
Condition number
Hermitian matrix
Eigenvalue
Eigenvalue problem
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ISSN0895-4798
1095-7162
DOI10.1137/S089547980139995X

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Summary:We present a chart of structured backward errors for approximate eigenpairs of singly and doubly structured eigenvalue problems. We aim to give, wherever possible, formulae that are inexpensive to compute so that they can be used routinely in practice. We identify a number of problems for which the structured backward error is within a factor $\sqrt{2}$ of the unstructured backward error. This paper collects, unifies, and extends existing work on this subject.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0895-4798
1095-7162
DOI:10.1137/S089547980139995X