%0 Journal Article
%A Di Napoli, Edoardo
%A Polizzi, Eric
%A Saad, Yousef
%T Efficient estimation of eigenvalue counts in an interval
%J Numerical linear algebra with applications
%V 23
%N 4
%@ 1070-5325
%C New York, NY [u.a.]
%I Wiley
%M FZJ-2016-04280
%P 674-692
%D 2016
%X 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.
%F PUB:(DE-HGF)16
%9 Journal Article
%U <Go to ISI:>//WOS:000383673200006
%R 10.1002/nla.2048
%U https://juser.fz-juelich.de/record/811979