{"paper":{"title":"Supremum-Norm Convergence for Step-Asynchronous Successive Overrelaxation on M-matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"cs.DS","authors_text":"Sebastiano Vigna","submitted_at":"2014-04-12T23:25:52Z","abstract_excerpt":"Step-asynchronous successive overrelaxation updates the values contained in a single vector using the usual Gau\\ss-Seidel-like weighted rule, but arbitrarily mixing old and new values, the only constraint being temporal coherence: you cannot use a value before it has been computed. We show that given a nonnegative real matrix $A$, a $\\sigma\\geq\\rho(A)$ and a vector $\\boldsymbol w>0$ such that $A\\boldsymbol w\\leq\\sigma\\boldsymbol w$, every iteration of step-asynchronous successive overrelaxation for the problem $(sI- A)\\boldsymbol x=\\boldsymbol b$, with $s >\\sigma$, reduces geometrically the $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3327","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"}