%0 Journal Article
%A Winkelmann, Jan
%A Di Napoli, Edoardo
%T Non-linear Least-Squares Optimization of Rational Filters for the Solution of Interior Hermitian Eigenvalue Problems
%J Frontiers in applied mathematics and statistics
%V 5
%@ 2297-4687
%C Lausanne
%I Frontiers Media
%M FZJ-2019-01374
%P 5
%D 2019
%X 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.
%F PUB:(DE-HGF)16
%9 Journal Article
%U <Go to ISI:>//WOS:001050584000001
%R 10.3389/fams.2019.00005
%U https://juser.fz-juelich.de/record/860709