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.
Author: | Volker Mehrmann, Hongguo Xu |
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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 |