Research articles
ScienceAsia 50 (2024):ID 2024049 1-10 |doi:
10.2306/scienceasia1513-1874.2024.049
An inexact Krylov subspace method for large generalized
Hankel eigenproblems
Zi-Yan Huang, Ting-Ting Feng*
ABSTRACT: Krylov subspace method is an effective method for large-scale eigenproblems. The shift-and-invert Arnoldi
method is employed to compute a few eigenpairs of a large Hankel matrix pencil. However, a crucial step in the process
is computing products between the inversion of a Hankel matrix and vectors. The inversion of the Hankel matrix can be
obtained by solving two Hankel systems. By establishing a relationship between the errors of systems and the residuals
of the Hankel eigenproblem, we provide a practical stopping criterion for solving Hankel systems and propose an inexact
shift-and-invert Arnoldi method for the generalized Hankel eigenproblem. Numerical experiments are presented to
demonstrate the efficiency of the new algorithm and our theoretical results.
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Department of Mathematics, School of Sciences, Hangzhou Dianzi University, Hangzhou 310018 China |
* Corresponding author, E-mail: ttfeng@hdu.edu.cn
Received 20 Jun 2023, Accepted 26 Jan 2024
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