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A Counterexample for Characterizing an Invariant Subspace by a Singularity System

Please always quote using this URN:urn:nbn:de:0296-matheon-4303
  • As an alternative to Newton's method an approach based on singularity theory can be exploited for computing a simple eigenvalue and corresponding eigenvectors of a nonnormal matrix $A$ in a stable way, see [Schwetlick/L\"osche, 2000]. In the paper it is shown by constructing a counterexample with an singular singularity system, that a straightforward extension of this technique to the computation of invariant subspaces of dimension $p>1$ will not work, in general. The finding of this counterexample required a detailed study of the linear block singularity operator.

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Metadaten
Author:Hubert Schwetlick, Kathrin Schreiber
URN:urn:nbn:de:0296-matheon-4303
Referee:Volker Mehrmann
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2007/12/12
Release Date:2007/07/12
Tag:
Institute:Technische Universität Berlin
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F15 Eigenvalues, eigenvectors
Preprint Number:419
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