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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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a 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