{"paper":{"title":"Computing the Action of Trigonometric and Hyperbolic Matrix Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Nicholas J. Higham, Peter Kandolf","submitted_at":"2016-07-14T06:58:04Z","abstract_excerpt":"We derive a new algorithm for computing the action $f(A)V$ of the cosine, sine, hyperbolic cosine, and hyperbolic sine of a matrix $A$ on a matrix $V$, without first computing $f(A)$. The algorithm can compute $\\cos(A)V$ and $\\sin(A)V$ simultaneously, and likewise for $\\cosh(A)V$ and $\\sinh(A)V$, and it uses only real arithmetic when $A$ is real. The algorithm exploits an existing algorithm \\texttt{expmv} of Al-Mohy and Higham for $\\mathrm{e}^AV$ and its underlying backward error analysis. Our experiments show that the new algorithm performs in a forward stable manner and is generally signific"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04012","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"}