Convergence Analysis of Extended LOBPCG for Computing Extreme Eigenvalues
Numerical Analysis
2023-03-03 v1 Numerical Analysis
Abstract
This paper is concerned with the convergence analysis of an extended variation of the locally optimal preconditioned conjugate gradient method (LOBPCG) for the extreme eigenvalue of a Hermitian matrix polynomial which admits some extended form of Rayleigh quotient. This work is a generalization of the analysis by Ovtchinnikov (SIAM J. Numer. Anal., 46(5):2567-2592, 2008). As instances, the algorithms for definite matrix pairs and hyperbolic quadratic matrix polynomials are shown to be globally convergent and to have an asymptotically local convergence rate. Also, numerical examples are given to illustrate the convergence.
Cite
@article{arxiv.2004.14002,
title = {Convergence Analysis of Extended LOBPCG for Computing Extreme Eigenvalues},
author = {Peter Benner and Xin Liang},
journal= {arXiv preprint arXiv:2004.14002},
year = {2023}
}
Comments
21 pages, 2 figures