TY  - JOUR
AU  - Di Napoli, Edoardo
AU  - Polizzi, Eric
AU  - Saad, Yousef
TI  - Efficient estimation of eigenvalue counts in an interval
JO  - Numerical linear algebra with applications
VL  - 23
IS  - 4
SN  - 1070-5325
CY  - New York, NY [u.a.]
PB  - Wiley
M1  - FZJ-2016-04280
SP  - 674-692
PY  - 2016
AB  - 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.
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:000383673200006
DO  - DOI:10.1002/nla.2048
UR  - https://juser.fz-juelich.de/record/811979
ER  -