A Thick-Restart Lanczos algorithm with polynomial filtering for Hermitian eigenvalue problems
Numerical Analysis
2015-12-29 v1
Abstract
Polynomial filtering can provide a highly effective means of computing all eigenvalues of a real symmetric (or complex Hermitian) matrix that are located in a given interval, anywhere in the spectrum. This paper describes a technique for tackling this problem by combining a Thick-Restart version of the Lanczos algorithm with deflation (`locking') and a new type of polynomial filters obtained from a least-squares technique. The resulting algorithm can be utilized in a `spectrum-slicing' approach whereby a very large number of eigenvalues and associated eigenvectors of the matrix are computed by extracting eigenpairs located in different sub-intervals independently from one another.
Cite
@article{arxiv.1512.08135,
title = {A Thick-Restart Lanczos algorithm with polynomial filtering for Hermitian eigenvalue problems},
author = {Ruipeng Li and Yuanzhe Xi and Eugene Vecharynski and Chao Yang and Yousef Saad},
journal= {arXiv preprint arXiv:1512.08135},
year = {2015}
}