TY  - JOUR
AU  - Kollnig, Konrad
AU  - Bientinesi, Paolo
AU  - Di Napoli, Edoardo
TI  - Rational Spectral Filters with Optimal Convergence Rate
JO  - SIAM journal on scientific computing
VL  - 43
IS  - 4
SN  - 0196-5204
CY  - Philadelphia, Pa.
PB  - SIAM
M1  - FZJ-2020-00420
SP  - A2660–A2684
PY  - 2021
AB  - 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.
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:000692204700003
DO  - DOI:10.1137/20M1313933
UR  - https://juser.fz-juelich.de/record/872963
ER  -