{"paper":{"title":"Efficient nuclear norm approximation via the randomized UTV algorithm","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Nathan Heavner, Per-Gunnar Martinsson","submitted_at":"2019-03-27T16:53:43Z","abstract_excerpt":"The recently introduced algorithm randUTV provides a highly efficient technique for computing accurate approximations to all the singular values of a given matrix $A$. The original version of randUTV was designed to compute a full factorization of the matrix in the form $A = UTV^*$ where $U$ and $V$ are orthogonal matrices, and $T$ is upper triangular. The estimates to the singular values of $A$ appear along the diagonal of $T$. This manuscript describes how the randUTV algorithm can be modified when the only quantity of interest being sought is the vector of approximate singular values. The r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.11543","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":""},"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"}