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Softw."],"published-print":{"date-parts":[[2016,6,15]]},"abstract":"<jats:p>\n            Bini-Capovani-Lotti-Romani approximate formula (or border rank) for matrix multiplication achieves a better complexity than Strassen\u2019s matrix multiplication formula. In this article, we show a novel way to use the approximate formula in the special case where the ring is\n            <jats:bold>Z<\/jats:bold>\n            \/\n            <jats:italic>p<\/jats:italic>\n            <jats:bold>Z<\/jats:bold>\n            . In addition, we show an implementation \u00e0 la FFLAS--FFPACK, where\n            <jats:italic>p<\/jats:italic>\n            is a word-size modulo, that improves on state-of-the-art\n            <jats:bold>Z<\/jats:bold>\n            \/\n            <jats:italic>p<\/jats:italic>\n            <jats:bold>Z<\/jats:bold>\n            matrix multiplication implementations.\n          <\/jats:p>","DOI":"10.1145\/2829947","type":"journal-article","created":{"date-parts":[[2016,6,15]],"date-time":"2016-06-15T19:32:01Z","timestamp":1466019121000},"page":"1-12","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["Matrix Multiplication Over Word-Size Modular Rings Using Approximate Formulas"],"prefix":"10.1145","volume":"42","author":[{"given":"Brice","family":"Boyer","sequence":"first","affiliation":[{"name":"North Carolina State University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jean-Guillaume","family":"Dumas","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Grenoble Alpes"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2016,6,15]]},"reference":[{"doi-asserted-by":"publisher","key":"e_1_2_1_1_1","DOI":"10.1007\/BF02575865"},{"doi-asserted-by":"publisher","key":"e_1_2_1_2_1","DOI":"10.1016\/0020-0190(79)90113-3"},{"doi-asserted-by":"publisher","key":"e_1_2_1_3_1","DOI":"10.1145\/1837934.1837987"},{"key":"e_1_2_1_5_1","series-title":"Lecture Notes in Computer Science, Vp;\/ 8592, Hoon Hong and Chee K","volume-title":"Proceedings of the 2014 International Congress of Mathematical Software (ICMS\u201914)","author":"Boyer Brice","unstructured":"Brice Boyer , Jean-Guillaume Dumas , Pascal Giorgi , Cl\u00e9ment Pernet , and B. David Saunders . 2014. Elements of design for containers and solutions in the LinBox library . In Proceedings of the 2014 International Congress of Mathematical Software (ICMS\u201914) , Lecture Notes in Computer Science, Vp;\/ 8592, Hoon Hong and Chee K . Yap (Eds.). Springer , Berlin , 654--662. DOI:http:\/\/dx.doi.org\/10.1007\/978-3-662-44199-2_98 10.1007\/978-3-662-44199-2_98 Brice Boyer, Jean-Guillaume Dumas, Pascal Giorgi, Cl\u00e9ment Pernet, and B. David Saunders. 2014. Elements of design for containers and solutions in the LinBox library. In Proceedings of the 2014 International Congress of Mathematical Software (ICMS\u201914), Lecture Notes in Computer Science, Vp;\/ 8592, Hoon Hong and Chee K. Yap (Eds.). Springer, Berlin, 654--662. 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