Taiwanese Journal of Mathematics


Zhongxiao Jia and Yuquan Sun

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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

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

First available in Project Euclid: 10 July 2017

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Zentralblatt MATH identifier

Primary: 65F15: Eigenvalues, eigenvectors

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


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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