{"paper":{"title":"Evaluation of resonances: adaptivity and AAA rational approximation of randomly scalarized boundary integral resolvents","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Lloyd N. Trefethen, Manuel A. Santana, Oscar P. Bruno","submitted_at":"2024-05-30T00:22:09Z","abstract_excerpt":"This paper presents a novel algorithm, based on use of rational approximants of a randomly scalarized boundary integral resolvent in conjunction with an adaptive search strategy and an exponentially convergent secant-method termination stage, for the evaluation of acoustic and electromagnetic resonances in open and closed cavities. The desired cavity resonances are obtained as the poles of associated rational approximants; both the approximants and their poles are obtained by means of the recently introduced AAA rational-approximation algorithm. In fact, the proposed resonance-search method ap"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.19582","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.19582/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}