Efficient estimation of eigenvalue counts in an interval
Numerical Analysis
2014-08-06 v2
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.
Cite
@article{arxiv.1308.4275,
title = {Efficient estimation of eigenvalue counts in an interval},
author = {Edoardo Di Napoli and Eric Polizzi and Yousef Saad},
journal= {arXiv preprint arXiv:1308.4275},
year = {2014}
}
Comments
24 pages and 8 figures. Submitted to Numerical Linear Algebra with Applications