Thick restarting the weighted harmonic Golub-Kahan-Lanczos algorithm for the linear response eigenvalue problem

Abstract

In this paper, we propose a weighted harmonic Golub-Kahan-Lanczos algorithm for the linear response eigenvalue problem (LREP). Convergence properties are established for the error bounds of the approximate eigenpairs. Moreover, we consider a practical thick-restart procedure to reduce the computational and memory costs and present a weighted harmonic Golub-Kahan-Lanczos algorithm with deflated restarting. Numerical tests show the efficiency of our new algorithms.