Efficient estimation of eigenvalue counts in an interval |
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| Authors: | Edoardo Di Napoli Eric Polizzi Yousef Saad |
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| Affiliation: | 1. Jülich Supercomputing Centre, Forschungszentrum Jülich, Jülich, Germany;2. Department of Electrical and Computer Engineering, University of Massachusetts, Amherst, MA, USA;3. Computer Science and Engineering, University of Minnesota, Twin Cities, MN, USA |
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| 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. Copyright © 2016 John Wiley & Sons, Ltd. |
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| Keywords: | eigenvalue count subspace projector stochastic trace estimate FEAST Chebyshev polynomials eigenproblem resolvent |
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