Structure preserving deflation of infinite eigenvalues in structured pencils

Please always quote using this URN:urn:nbn:de:0296-matheon-12765
  • The long standing problem is discussed of how to deflate the part associated with the eigenvalue infinity in a structured matrix pencil using structure preserving unitary transformations. We derive such a deflation procedure and apply this new technique to symmetric, Hermitian or alternating pencils and in a modified form to (anti)-palindromic pencils. We present a detailed error and perturbation analysis of this and other deflation procedures and demonstrate the properties of the new algorithm with several numerical examples.

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Metadaten
Author:Volker Mehrmann, Hongguo Xu
URN:urn:nbn:de:0296-matheon-12765
Referee:Peter Deuflhard
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2014/03/22
Release Date:2014/03/22
Tag:structured staircase form, structured Kronecker canonical form, symmetric pencil, Hermitian pencil, alternating pencil, palindromic pencil, linear quadratic control, $H_\infty$ control
Institute:Technische Universität Berlin
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F15 Eigenvalues, eigenvectors
Preprint Number:1052
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