JSIAM Letters
Online ISSN : 1883-0617
Print ISSN : 1883-0609
Articles
Filter analysis for the stochastic estimation of eigenvalue counts
Yasuyuki MaedaYasunori FutamuraAkira ImakuraTetsuya Sakurai
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2015 Volume 7 Pages 53-56

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Abstract

To estimate the number of eigenvalues of a Hermitian matrix that are located in a given interval, existing methods include polynomial filtering and rational filtering. Both filtering approaches are based on stochastic approximations for matrix trace. In this paper, we analyze a rational filtering method that is based on polynomial filtering in which the solutions to the linear systems are approximated by a Krylov subspace method. Our analysis and numerical experiments indicate that the rational filtering method is effective when the eigenvalues of a given matrix are sparsely distributed in the target interval.

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© 2015, The Japan Society for Industrial and Applied Mathematics
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