1. Efficient estimation of eigenvalue counts in an interval
- Author
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Eric Polizzi, Yousef Saad, and Edoardo Di Napoli
- Subjects
Estimation ,Mathematical optimization ,Chebyshev polynomials ,Polynomial ,Algebra and Number Theory ,Applied Mathematics ,020206 networking & telecommunications ,010103 numerical & computational mathematics ,02 engineering and technology ,Interval (mathematics) ,01 natural sciences ,Hermitian matrix ,Task (project management) ,Public records ,0202 electrical engineering, electronic engineering, information engineering ,Applied mathematics ,0101 mathematics ,Eigenvalues and eigenvectors ,Mathematics - Abstract
Summary 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.
- Published
- 2016