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000872963 1001_ $$0P:(DE-HGF)0$$aKollnig, Konrad$$b0
000872963 245__ $$aRational Spectral Filters with Optimal Convergence Rate
000872963 260__ $$aPhiladelphia, Pa.$$bSIAM$$c2021
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000872963 520__ $$aIn 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.
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000872963 536__ $$0G:(DE-Juel1)SDLQM$$aSimulation and Data Laboratory Quantum Materials (SDLQM) (SDLQM)$$cSDLQM$$fSimulation and Data Laboratory Quantum Materials (SDLQM)$$x2
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000872963 7001_ $$0P:(DE-HGF)0$$aBientinesi, Paolo$$b1
000872963 7001_ $$0P:(DE-Juel1)144723$$aDi Napoli, Edoardo$$b2$$eCorresponding author
000872963 773__ $$0PERI:(DE-600)1468391-x$$a10.1137/20M1313933$$gVol. 43, no. 4, p. A2660 - A2684$$n4$$pA2660–A2684$$tSIAM journal on scientific computing$$v43$$x0196-5204$$y2021
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