Journal Article

FZJ-2019-01374

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Non-linear Least-Squares Optimization of Rational Filters for the Solution of Interior Hermitian Eigenvalue Problems

Winkelmann, J.RWTH* ; Di Napoli, E. (Corresponding author)FZJ*

2019
Frontiers Media Lausanne

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Please use a persistent id in citations: http://hdl.handle.net/2128/21730  doi:10.3389/fams.2019.00005

Abstract: Rational filter functions can be used to improve convergence of contour-based eigensolvers, a popular family of algorithms for the solution of the interior eigenvalue problem. We present a framework for the optimization of rational filters based on a non-convexweighted Least-Squares scheme. When used in combination with a contour based eigensolvers library, our filters out-perform existing ones on a large and representative set of benchmark problems. This work provides a detailed description of: (1) a set up of the optimization process that exploits symmetries of the filter function for Hermitian eigenproblems, (2) a formulation of the gradient descent and Levenberg-Marquardt algorithms that exploits the symmetries, (3) a method to select the starting position for theoptimization algorithms that reliably produces effective filters, (4) a constrained optimization scheme that produces filter functions with specific properties that may be beneficial to the performance of the eigensolver that employs them.

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Contributing Institute(s):

1. Jülich Supercomputing Center (JSC)
2. JARA - HPC (JARA-HPC)

Appears in the scientific report 2019

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