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A Thick-Restart Lanczos algorithm with polynomial filtering for Hermitian eigenvalue problems

Research paper by Ruipeng Li, Yuanzhe Xi, Eugene Vecharynski, Chao Yang, Yousef Saad

Indexed on: 26 Dec '15Published on: 26 Dec '15Published in: Mathematics - Numerical Analysis



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.