{"paper":{"title":"A Fast-Convergence Resolution of the Stochastic Eigenproblem Using Halley's Method and the Spectral-Chaos Approach","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Guang Lin, Hugo Esquivel, Kabir Oluwatobi Idowu","submitted_at":"2026-06-24T20:52:29Z","abstract_excerpt":"Solving stochastic eigenvalue problems has long been essential for informed decision-making, advancing scientific knowledge, and ensuring the reliability of engineering designs and applications. This paper underscores the need to continue enhancing existing numerical methods for solving the stochastic eigenproblem in order to improve convergence rates, computational efficiency, and robustness. Specifically, we propose a novel spectral-chaos method for solving the stochastic (linear) eigenvalue problem, employing Halley's method as the root-finding algorithm to leverage its cubic convergence pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.26375","kind":"arxiv","version":1},"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/2606.26375/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"}