{"paper":{"title":"The shift-and-invert Arnoldi method for singular matrix pencils","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Karl Meerbergen, Zhijun Wang","submitted_at":"2024-11-05T08:17:18Z","abstract_excerpt":"A popular method for solving large sparse regular eigenvalue problem is the shift-and-invert Arnoldi method. This paper aims to use the method for large sparse singular pencils. In three recent papers, {\\em Hochstenbach, Mehl, and Plestenjak, 2019, 2023, and 2024}, propose regularization of the singular pencil, using randomly chosen regularization matrices. We propose sparse regularization matrices obtained from the pivoting sequence of a sparse LU factorization. As a side effect, the LU factorization often is rank revealing, which facilitates finding a regularization. Numerical examples illus"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.02895","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/2411.02895/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"}