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000860709 1001_ $$0P:(DE-HGF)0$$aWinkelmann, Jan$$b0
000860709 245__ $$aNon-linear Least-Squares Optimization of Rational Filters for the Solution of Interior Hermitian Eigenvalue Problems
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000860709 520__ $$aRational filter functions can be used to improve convergence of contour-based eigensolvers, a popular family of algorithms for the solution of the interior eigenvalue problem. We present a framework for the optimization of rational filters based on a non-convexweighted Least-Squares scheme. When used in combination with a contour based eigensolvers library, our filters out-perform existing ones on a large and representative set of benchmark problems. This work provides a detailed description of: (1) a set up of the optimization process that exploits symmetries of the filter function for Hermitian eigenproblems, (2) a formulation of the gradient descent and Levenberg-Marquardt algorithms that exploits the symmetries, (3) a method to select the starting position for theoptimization algorithms that reliably produces effective filters, (4) a constrained optimization scheme that produces filter functions with specific properties that may be beneficial to the performance of the eigensolver that employs them.
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000860709 7001_ $$0P:(DE-Juel1)144723$$aDi Napoli, Edoardo$$b1$$eCorresponding author$$ufzj
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