{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T21:54:43Z","timestamp":1740174883523,"version":"3.37.3"},"reference-count":0,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2000,1,1]],"date-time":"2000-01-01T00:00:00Z","timestamp":946684800000},"content-version":"vor","delay-in-days":1826,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/100006133","name":"Advanced Research Projects Agency - Energy","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100006133","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000161","name":"National Institute of Standards and Technology","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000161","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Scientific Programming"],"published-print":{"date-parts":[[1995,1]]},"abstract":"<jats:p>In this article, we present a program generation strategy of Strassen\u2032s matrix multiplication algorithm using a programming methodology based on tensor product formulas. In this methodology, block recursive programs such as the fast Fourier Transforms and Strassen\u2032s matrix multiplication algorithm are expressed as algebraic formulas involving tensor products and other matrix operations. Such formulas can be systematically translated to high\u2010performance parallel\/vector codes for various architectures. In this article, we present a nonrecursive implementation of Strassen\u2032s algorithm for shared memory vector processors such as the Cray Y\u2010MP. A previous implementation of Strassen\u2032s algorithm synthesized from tensor product formulas required working storage of size O(7<jats:sup>n<\/jats:sup>) for multiplying 2<jats:sup>n<\/jats:sup> \u00d7 2<jats:sup>n<\/jats:sup> matrices. We present a modified formulation in which the working storage requirement is reduced to O(4<jats:sup>n<\/jats:sup>). The modified formulation exhibits sufficient parallelism for efficient implementation on a shared memory multiprocessor. Performance results on a Cray Y\u2010MP8\/64 are presented.<\/jats:p>","DOI":"10.1155\/1995\/636457","type":"journal-article","created":{"date-parts":[[2015,1,12]],"date-time":"2015-01-12T14:11:41Z","timestamp":1421071901000},"page":"275-289","source":"Crossref","is-referenced-by-count":11,"title":["A Tensor Product Formulation of Strassen\u2032s Matrix Multiplication Algorithm with Memory Reduction"],"prefix":"10.1155","volume":"4","author":[{"given":"B.","family":"Kumar","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"C.-H.","family":"Huang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P.","family":"Sadayappan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"R.W.","family":"Johnson","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[1995,4,17]]},"container-title":["Scientific Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/sp\/1995\/636457.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/1995\/636457","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,8]],"date-time":"2024-08-08T03:46:45Z","timestamp":1723088805000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/1995\/636457"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,1]]},"references-count":0,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1995,1]]}},"alternative-id":["10.1155\/1995\/636457"],"URL":"https:\/\/doi.org\/10.1155\/1995\/636457","archive":["Portico"],"relation":{},"ISSN":["1058-9244","1875-919X"],"issn-type":[{"type":"print","value":"1058-9244"},{"type":"electronic","value":"1875-919X"}],"subject":[],"published":{"date-parts":[[1995,1]]}}}