{"paper":{"title":"Performance evaluation of multiple precision matrix multiplications using parallelized Strassen and Winograd algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.MS","cs.NA"],"primary_cat":"math.NA","authors_text":"Tomonori Kouya","submitted_at":"2015-10-29T10:58:55Z","abstract_excerpt":"It is well known that Strassen and Winograd algorithms can reduce the computational costs associated with dense matrix multiplication. We have already shown that they are also very effective for software-based multiple precision floating-point arithmetic environments such as the MPFR/GMP library. In this paper, we show that we can obtain the same effectiveness for double-double (DD) and quadruple-double (QD) environments supported by the QD library, and that parallelization can increase the speed of these multiple precision matrix multiplications. Finally, we demonstrate that our implemented p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08642","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"}