% IMPORTANT: The following is UTF-8 encoded. This means that in the presence % of non-ASCII characters, it will not work with BibTeX 0.99 or older. % Instead, you should use an up-to-date BibTeX implementation like “bibtex8” or % “biber”. @ARTICLE{DiNapoli:811979, author = {Di Napoli, Edoardo and Polizzi, Eric and Saad, Yousef}, title = {{E}fficient estimation of eigenvalue counts in an interval}, journal = {Numerical linear algebra with applications}, volume = {23}, number = {4}, issn = {1070-5325}, address = {New York, NY [u.a.]}, publisher = {Wiley}, reportid = {FZJ-2016-04280}, pages = {674-692}, year = {2016}, 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. We also discuss how the latter method is particularly well- suited for the FEAST eigensolver.}, cin = {JSC}, ddc = {510}, cid = {I:(DE-Juel1)JSC-20090406}, pnm = {511 - Computational Science and Mathematical Methods (POF3-511) / Simulation and Data Laboratory Quantum Materials (SDLQM) (SDLQM)}, pid = {G:(DE-HGF)POF3-511 / G:(DE-Juel1)SDLQM}, typ = {PUB:(DE-HGF)16}, UT = {WOS:000383673200006}, doi = {10.1002/nla.2048}, url = {https://juser.fz-juelich.de/record/811979}, }