An inexact Krylov subspace method for large generalized Hankel eigenproblems

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.