Structured Condition Numbers for Invariant Subspaces

Invariant subspaces of structured matrices are sometimes better conditioned with respect to structured perturbations than with respect to general perturbations. Sometimes they are not. This paper proposes an appropriate condition number $c_{\S}$, for invariant subspaces subject to structured perturb...

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Published inSIAM journal on matrix analysis and applications Vol. 28; no. 2; pp. 326 - 347
Main Authors Byers, Ralph, Kressner, Daniel
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.01.2006
Subjects
Applied mathematics
Decomposition
Eigenvalues
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ISSN0895-4798
1095-7162
DOI10.1137/050637601

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Abstract Invariant subspaces of structured matrices are sometimes better conditioned with respect to structured perturbations than with respect to general perturbations. Sometimes they are not. This paper proposes an appropriate condition number $c_{\S}$, for invariant subspaces subject to structured perturbations. Several examples compare $c_{\S}$ with the unstructured condition number. The examples include block cyclic, Hamiltonian, and orthogonal matrices. This approach extends naturally to structured generalized eigenvalue problems such as palindromic matrix pencils.
AbstractList Invariant subspaces of structured matrices are sometimes better conditioned with respect to structured perturbations than with respect to general perturbations. Sometimes they are not. This paper proposes an appropriate condition number $c_{\S}$, for invariant subspaces subject to structured perturbations. Several examples compare $c_{\S}$ with the unstructured condition number. The examples include block cyclic, Hamiltonian, and orthogonal matrices. This approach extends naturally to structured generalized eigenvalue problems such as palindromic matrix pencils.
Author Kressner, Daniel
Byers, Ralph
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SubjectTerms Applied mathematics
Decomposition
Eigenvalues
Title Structured Condition Numbers for Invariant Subspaces
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