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| Journal Article | FZJ-2016-04280 |
; ;
2016
Wiley
New York, NY [u.a.]
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Please use a persistent id in citations: doi:10.1002/nla.2048
Abstract: Estimating the number of eigenvalues located in a given interval of a large sparse Hermitian matrix is an important problem in certain applications, and it is a prerequisite of eigensolvers based on a divide-and-conquer paradigm. Often, an exact count is not necessary, and methods based on stochastic estimates can be utilized to yield rough approximations. This paper examines a number of techniques tailored to this specific task. It reviews standard approaches and explores new ones based on polynomial and rational approximation filtering combined with a stochastic procedure. We also discuss how the latter method is particularly well- suited for the FEAST eigensolver.
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