On the permissible arrangements of Ritz values for normal matrices in the complex plane

This article discusses Ritz and harmonic Ritz values computed from a Krylov subspace, generated by a normal matrix. We give necessary and sufficient conditions for a given tuple of complex numbers to represent Ritz values: the existence of a positive solution to a certain linear system with a Cauchy...

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Bibliographic Details
Published inLinear algebra and its applications Vol. 438; no. 12; pp. 4606 - 4624
Main Author Bujanović, Zvonimir
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.06.2013
Subjects
Arnoldi algorithm
Eigenvalues
Harmonic Ritz values
Krylov subspaces
Ritz values
15A42
Arnoldi algorithm
Krylov subspaces
Eigenvalues
65F15
Harmonic Ritz values
Ritz values
65F18
15A18
15A29
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Summary:This article discusses Ritz and harmonic Ritz values computed from a Krylov subspace, generated by a normal matrix. We give necessary and sufficient conditions for a given tuple of complex numbers to represent Ritz values: the existence of a positive solution to a certain linear system with a Cauchy matrix. Using this characterization, we prove several localization results for the Ritz values of normal matrices and discuss consequences for the convergence of the restarted Arnoldi algorithm. Similar results are shown for the harmonic case as well.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2013.02.014