Efficient estimation of eigenvalue counts in an interval
Copyright policy )Efficient estimation of eigenvalue counts in an interval
SummaryEstimating 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.
- University of Minnesota Morris United States
- Helmholtz Association of German Research Centres Germany
- University of Massachusetts System United States
- Forschungszentrum Jülich Germany
- University of Minnesota United States
Numerical computation of eigenvalues and eigenvectors of matrices, Numerical Analysis, Numerical Analysis (math.NA), subspace projector, eigenproblem resolvent, Computational methods for sparse matrices, FEAST, FOS: Mathematics, Hermitian, skew-Hermitian, and related matrices, Chebyshev polynomials, stochastic trace estimate, eigenvalue count
Numerical computation of eigenvalues and eigenvectors of matrices, Numerical Analysis, Numerical Analysis (math.NA), subspace projector, eigenproblem resolvent, Computational methods for sparse matrices, FEAST, FOS: Mathematics, Hermitian, skew-Hermitian, and related matrices, Chebyshev polynomials, stochastic trace estimate, eigenvalue count
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