Volume 51, pp. 529-546, 2019.

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

Hong-Xiu Zhong and Guo-Liang Chen

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.

Full Text (PDF) [361 KB], BibTeX

Key words

linear response eigenvalue problem, harmonic Rayleigh-Ritz projection, weighted Golub-Kahan-Lanczos algorithm, thick restart

AMS subject classifications

65F15, 65F50, 15A18

Links to the cited ETNA articles

[28]	Vol. 47 (2017), pp. 153-178 Hong-Xiu Zhong and Hongguo Xu: Weighted Golub-Kahan-Lanczos bidiagonalization algorithms

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