{"paper":{"title":"Non-Linear Least-Squares Optimization of Rational Filters for the Solution of Interior Eigenvalue Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"cs.CE","authors_text":"2) ((1) AICES, (2) JSC, Edoardo Di Napoli (1, Forschungszentrum J\\\"ulich), Jan Winkelmann (1), RWTH Aachen University","submitted_at":"2017-04-11T12:02:21Z","abstract_excerpt":"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-convex weighted Least-Squares scheme. When used in combination with the FEAST 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,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03255","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}