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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Bibliographic Details
Published inTaiwanese journal of mathematics Vol. 17; no. 1; pp. 259 - 274
Main Authors Jia, Zhongxiao, Sun, Yuquan
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.02.2013
Subjects
Algorithms
Approximation
Eigenvalues
Eigenvectors
Linear algebra
Matrices
Numerical methods
Pencils
Spectral theory
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ISSN1027-5487
2224-6851
DOI10.11650/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.
ISSN:1027-5487
2224-6851
DOI:10.11650/tjm.17.2013.1949