Taiwanese Journal of Mathematics

SHIRRA: A REFINED VARIANT OF SHIRA FOR THE SKEW-HAMILTONIAN/HAMILTONIAN (SHH) PENCIL EIGENVALUE PROBLEM

Zhongxiao Jia and Yuquan Sun

Full-text: Open access

Abstract

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.

Article information

Source
Taiwanese J. Math., Volume 17, Number 1 (2013), 259-274.

Dates
First available in Project Euclid: 10 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499705886

Digital Object Identifier
doi:10.11650/tjm.17.2013.1949

Mathematical Reviews number (MathSciNet)
MR3028868

Zentralblatt MATH identifier
1264.65053

Subjects
Primary: 65F15: Eigenvalues, eigenvectors

Keywords
refined projection SHH pencil quadratic eigenvalue problem Ritz value refined eigenvector approximation implicit restart refined shifts exact shifts

Citation

Jia, Zhongxiao; Sun, Yuquan. SHIRRA: A REFINED VARIANT OF SHIRA FOR THE SKEW-HAMILTONIAN/HAMILTONIAN (SHH) PENCIL EIGENVALUE PROBLEM. Taiwanese J. Math. 17 (2013), no. 1, 259--274. doi:10.11650/tjm.17.2013.1949. https://projecteuclid.org/euclid.twjm/1499705886


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