TY  - JOUR
AU  - Winkelmann, Jan
AU  - Di Napoli, Edoardo
TI  - Non-linear Least-Squares Optimization of Rational Filters for the Solution of Interior Hermitian Eigenvalue Problems
JO  - Frontiers in applied mathematics and statistics
VL  - 5
SN  - 2297-4687
CY  - Lausanne
PB  - Frontiers Media
M1  - FZJ-2019-01374
SP  - 5
PY  - 2019
AB  - 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.
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:001050584000001
DO  - DOI:10.3389/fams.2019.00005
UR  - https://juser.fz-juelich.de/record/860709
ER  -