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Polynomial filtering can provide a highly effective means of computing alleigenvalues of a real symmetric (or complex Hermitian) matrix that are locatedin a given interval, anywhere in the spectrum. This paper describes a techniquefor tackling this problem by combining a Thick-Restart version of the Lanczosalgorithm with deflation (`locking') and a new type of polynomial filtersobtained from a least-squares technique. The resulting algorithm can beutilized in a `spectrum-slicing' approach whereby a very large number ofeigenvalues and associated eigenvectors of the matrix are computed byextracting eigenpairs located in different sub-intervals independently from oneanother.

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