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 -