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A THICK-RESTART LANCZOS ALGORITHM WITH POLYNOMIAL FILTERING FOR HERMITIAN EIGENVALUE PROBLEMS
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DOI：10.1137/15M1054493.png)
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Abstract
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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 filter 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 subintervals independently from one another.
Keywords:
Lanczos algorithm
polynomial filtering
thick-restart
deflation
spectrum slicing
interior eigenvalue problems
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