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Efficient estimation of eigenvalue counts in an interval · Around

2013

Efficient estimation of eigenvalue counts in an interval

Di Napoli, Edoardo, Polizzi, Eric, Saad, Yousef

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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.

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