%0 Journal Article
%A Kollnig, Konrad
%A Bientinesi, Paolo
%A Di Napoli, Edoardo
%T Rational Spectral Filters with Optimal Convergence Rate
%J SIAM journal on scientific computing
%V 43
%N 4
%@ 0196-5204
%C Philadelphia, Pa.
%I SIAM
%M FZJ-2020-00420
%P A2660–A2684
%D 2021
%X In recent years, contour-based eigensolvers have emerged as a standard approach for the solution of large and sparse eigenvalue problems. Building upon recent performance improvements through nonlinear least-squares optimization of so-called rational filters, we introduce a systematic method to design these filters by minimizing the worst-case convergence rate and eliminate the parametric dependence on weight functions. Further, we provide an efficient way to deal with the box-constraints which play a central role for the use of iterative linear solvers in contour-based eigensolvers. Indeed, these parameter-free filters consistently minimize the number of iterations and the number of FLOPs to reach convergence in the eigensolver. As a byproduct, our rational filters allow for a simple solution to load balancing when the solution of an interior eigenproblem is approached by the slicing of the sought after spectral interval.
%F PUB:(DE-HGF)16
%9 Journal Article
%U <Go to ISI:>//WOS:000692204700003
%R 10.1137/20M1313933
%U https://juser.fz-juelich.de/record/872963