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Implicit QR Algorithms for Palindromic and Even Eigenvalue Problems

Please always quote using this URN:urn:nbn:de:0296-matheon-4493
  • In the spirit of the Hamiltonian QR algorithm and other bidirectional chasing algorithms, a structure-preserving variant of the implicit QR algorithm for palindromic eigenvalue problems is proposed. This new palindromic QR algorithm is strongly backward stable and requires less operations than the standard QZ algorithm, but is restricted to matrix classes where a preliminary reduction to structured Hessenberg form can be performed. By an extension of the implicit Q theorem, the palindromic QR algorithm is shown to be equivalent to a previously developed explicit version. Also, the classical convergence theory for the QR algorithm can be extended to prove local quadratic convergence. We briefly demonstrate how even eigenvalue problems can be addressed by similar techniques.

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Metadaten
Author:Daniel Kressner, Christian Schröder, David S. Watkins
URN:urn:nbn:de:0296-matheon-4493
Referee:Volker Mehrmann
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2008/01/24
Release Date:2008/01/24
Tag:
Institute:Technische Universität Berlin
MSC-Classification:15-XX LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY / 15Axx Basic linear algebra / 15A18 Eigenvalues, singular values, and eigenvectors
15-XX LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY / 15Axx Basic linear algebra / 15A22 Matrix pencils [See also 47A56]
15-XX LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY / 15Axx Basic linear algebra / 15A23 Factorization of matrices
65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F15 Eigenvalues, eigenvectors
Preprint Number:432
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