SHIRRA: A REFINED VARIANT OF SHIRA FOR THE SKEW-HAMILTONIAN/HAMILTONIAN (SHH) PENCIL EIGENVALUE PROBLEM
Combining the Skew-Hamiltonian Isotropic implicitly Restarted Arnoldi algorithm (SHIRA) due to Mehrmann and Waktins and the refined projection principle proposed by the first author, we present a Skew-Hamiltonian Isotropic implicitly Restarted Refined Arnoldi algorithm (SHIRRA) for the skew-Hamilton...
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Published in | Taiwanese journal of mathematics Vol. 17; no. 1; pp. 259 - 274 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Mathematical Society of the Republic of China
01.02.2013
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Subjects | |
Online Access | Get full text |
ISSN | 1027-5487 2224-6851 |
DOI | 10.11650/tjm.17.2013.1949 |
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Summary: | Combining the Skew-Hamiltonian Isotropic implicitly Restarted Arnoldi algorithm (SHIRA) due to Mehrmann and Waktins and the refined projection principle proposed by the first author, we present a Skew-Hamiltonian Isotropic implicitly Restarted Refined Arnoldi algorithm (SHIRRA) for the skew-Hamiltonian/Hamiltonian (SHH) pencil eigenvalue problem. Within SHIRRA, we propose new shifts, called refined shifts, that are theoretically better and numerically more efficient than the exact shifts used within SHIRA. Numerical examples illustrate the efficiency and superiority of SHIRRA.
2010Mathematics Subject Classification: 65F15.
Key words and phrases: Refined projection, SHH pencil, Quadratic eigenvalue problem, Ritz value, Refined eigenvector approximation, Implicit restart, Refined shifts, Exact shifts. |
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ISSN: | 1027-5487 2224-6851 |
DOI: | 10.11650/tjm.17.2013.1949 |