{"id":"https://openalex.org/W2430670595","doi":"https://doi.org/10.1145/2829947","title":"Matrix Multiplication Over Word-Size Modular Rings Using Approximate Formulas","display_name":"Matrix Multiplication Over Word-Size Modular Rings Using Approximate Formulas","publication_year":2016,"publication_date":"2016-06-15","ids":{"openalex":"https://openalex.org/W2430670595","doi":"https://doi.org/10.1145/2829947","mag":"2430670595"},"language":"en","primary_location":{"id":"doi:10.1145/2829947","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2829947","pdf_url":null,"source":{"id":"https://openalex.org/S163326656","display_name":"ACM Transactions on Mathematical Software","issn_l":"0098-3500","issn":["0098-3500","1557-7295"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Mathematical Software","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-00987812","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016706681","display_name":"Brice Boyer","orcid":null},"institutions":[{"id":"https://openalex.org/I137902535","display_name":"North Carolina State University","ror":"https://ror.org/04tj63d06","country_code":"US","type":"education","lineage":["https://openalex.org/I137902535"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Brice Boyer","raw_affiliation_strings":["North Carolina State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"North Carolina State University","institution_ids":["https://openalex.org/I137902535"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091337059","display_name":"Jean\u2010Guillaume Dumas","orcid":"https://orcid.org/0000-0002-2591-172X"},"institutions":[{"id":"https://openalex.org/I4400008911","display_name":"Institut des langues et cultures d'Europe, Am\u00e9rique, Afrique, Asie et Australie","ror":"https://ror.org/02bxdh068","country_code":"FR","type":"facility","lineage":["https://openalex.org/I4400008911"]},{"id":"https://openalex.org/I899635006","display_name":"Universit\u00e9 Grenoble Alpes","ror":"https://ror.org/02rx3b187","country_code":"FR","type":"education","lineage":["https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Jean-Guillaume Dumas","raw_affiliation_strings":["Universit\u00e9 Grenoble Alpes"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Grenoble Alpes","institution_ids":["https://openalex.org/I899635006","https://openalex.org/I4400008911"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2818,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.78607825,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"42","issue":"3","first_page":"1","last_page":"12"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/strassen-algorithm","display_name":"Strassen algorithm","score":0.946274995803833},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.6965819001197815},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.6709210276603699},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6446287035942078},{"id":"https://openalex.org/keywords/multiplication-algorithm","display_name":"Multiplication algorithm","score":0.6139058470726013},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.6131935715675354},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5786804556846619},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5720068216323853},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.5653083324432373},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.5213043093681335},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35979723930358887},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35679590702056885},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3302273154258728},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.29986029863357544},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.16626253724098206},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.056423962116241455},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.055161893367767334}],"concepts":[{"id":"https://openalex.org/C39096654","wikidata":"https://www.wikidata.org/wiki/Q728507","display_name":"Strassen algorithm","level":4,"score":0.946274995803833},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.6965819001197815},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.6709210276603699},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6446287035942078},{"id":"https://openalex.org/C201290732","wikidata":"https://www.wikidata.org/wiki/Q130762","display_name":"Multiplication algorithm","level":3,"score":0.6139058470726013},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.6131935715675354},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5786804556846619},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5720068216323853},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.5653083324432373},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.5213043093681335},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35979723930358887},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35679590702056885},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3302273154258728},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.29986029863357544},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.16626253724098206},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.056423962116241455},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.055161893367767334},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/2829947","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2829947","pdf_url":null,"source":{"id":"https://openalex.org/S163326656","display_name":"ACM Transactions on Mathematical Software","issn_l":"0098-3500","issn":["0098-3500","1557-7295"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Mathematical Software","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-00987812v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00987812","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ACM Transactions on Mathematical Software, 2016, 42 (3-20), ⟨10.1145/2829947⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-00987812v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00987812","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ACM Transactions on Mathematical Software, 2016, 42 (3-20), ⟨10.1145/2829947⟩","raw_type":"Journal articles"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W16349279","https://openalex.org/W1996440503","https://openalex.org/W2002048434","https://openalex.org/W2004916460","https://openalex.org/W2035476608","https://openalex.org/W2040829540","https://openalex.org/W2053839977","https://openalex.org/W2056035813","https://openalex.org/W2065815779","https://openalex.org/W2069906535","https://openalex.org/W2145889866","https://openalex.org/W2150343316"],"related_works":["https://openalex.org/W2170716619","https://openalex.org/W2145889866","https://openalex.org/W2949595835","https://openalex.org/W2039853057","https://openalex.org/W2392656174","https://openalex.org/W3204033665","https://openalex.org/W2269364368","https://openalex.org/W2032839380","https://openalex.org/W1809313304","https://openalex.org/W4301181185"],"abstract_inverted_index":{"Bini-Capovani-Lotti-Romani":[0],"approximate":[1,29],"formula":[2,30],"(or":[3],"border":[4],"rank)":[5],"for":[6],"matrix":[7,15,67],"multiplication":[8,16,68],"achieves":[9],"a":[10,23,56],"better":[11],"complexity":[12],"than":[13],"Strassen\u2019s":[14],"formula.":[17],"In":[18,44],"this":[19],"article,":[20],"we":[21,46],"show":[22,47],"novel":[24],"way":[25],"to":[26],"use":[27],"the":[28,32,36],"in":[31],"special":[33],"case":[34],"where":[35,53],"ring":[37],"is":[38,55],"Z":[39,42,63,66],"/":[40,64],"p":[41,54,65],".":[43],"addition,":[45],"an":[48],"implementation":[49],"\u00e0":[50],"la":[51],"FFLAS--FFPACK,":[52],"word-size":[57],"modulo,":[58],"that":[59],"improves":[60],"on":[61],"state-of-the-art":[62],"implementations.":[69]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2016-06-24T00:00:00"}