{"paper":{"title":"Low-rank updates of matrix functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI"],"primary_cat":"math.NA","authors_text":"Bernhard Beckermann, Daniel Kressner, Marcel Schweitzer","submitted_at":"2017-07-10T20:08:48Z","abstract_excerpt":"We consider the task of updating a matrix function $f(A)$ when the matrix $A\\in{\\mathbb C}^{n \\times n}$ is subject to a low-rank modification. In other words, we aim at approximating $f(A+D)-f(A)$ for a matrix $D$ of rank $k \\ll n$. The approach proposed in this paper attains efficiency by projecting onto tensorized Krylov subspaces produced by matrix-vector multiplications with $A$ and $A^*$. We prove the approximations obtained from $m$ steps of the proposed methods are exact if $f$ is a polynomial of degree at most $m$ and use this as a basis for proving a variety of convergence results, i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03045","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"}