Rational Spectral Filters with Optimal Convergence Rate

SIAM Journal on Scientific Computing, vol. 43, pp. A2660–A2684

Abstract

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.

Authors 3

1. Konrad Kollnig Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University

2. Paolo Bientinesi

   Umeå University

   Affiliation as printed

   UMEÅ UNIVERSITY

3. Edoardo Di Napoli

   Forschungszentrum Jülich · Jülich Supercomputing Centre

   Affiliation as printed

   Juelich Supercomputing Centre, Forschungszentrum Juelich