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000811979 1001_ $$0P:(DE-Juel1)144723$$aDi Napoli, Edoardo$$b0$$eCorresponding author$$ufzj
000811979 245__ $$aEfficient estimation of eigenvalue counts in an interval
000811979 260__ $$aNew York, NY [u.a.]$$bWiley$$c2016
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000811979 520__ $$aEstimating 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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000811979 536__ $$0G:(DE-Juel1)SDLQM$$aSimulation and Data Laboratory Quantum Materials (SDLQM) (SDLQM)$$cSDLQM$$fSimulation and Data Laboratory Quantum Materials (SDLQM)$$x2
000811979 7001_ $$0P:(DE-HGF)0$$aPolizzi, Eric$$b1
000811979 7001_ $$0P:(DE-HGF)0$$aSaad, Yousef$$b2
000811979 773__ $$0PERI:(DE-600)2012602-5$$a10.1002/nla.2048$$n4$$p674-692$$tNumerical linear algebra with applications$$v23$$x1070-5325$$y2016
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