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DOE OSTI · 1438696

A Thick-Restart Lanczos Algorithm with Polynomial Filtering for Hermitian Eigenvalue Problems

Li, Ruipeng·Xi, Yuanzhe·Vecharynski, Eugene·Yang, Chao·Saad, Yousef
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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 filter obtained from a least-squares technique. Furthermore, 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.

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97 MATHEMATICS AND COMPUTINGLanczos algorithmThick-Restartdeflationinterior eigenvalue problemspolynomial filteringspectrum slicing

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Li, Ruipeng, Xi, Yuanzhe, Vecharynski, Eugene, Yang, Chao, Saad, Yousef. 2016-08-16. A Thick-Restart Lanczos Algorithm with Polynomial Filtering for Hermitian Eigenvalue Problems. https://doi.org/10.1137/15m1054493

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