{"id":"https://openalex.org/W4391631734","doi":"https://doi.org/10.1145/3666000.3669697","title":"Strassen's algorithm is not optimally accurate","display_name":"Strassen's algorithm is not optimally accurate","publication_year":2024,"publication_date":"2024-07-15","ids":{"openalex":"https://openalex.org/W4391631734","doi":"https://doi.org/10.1145/3666000.3669697"},"language":"en","primary_location":{"id":"doi:10.1145/3666000.3669697","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3666000.3669697","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2024 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2402.05630","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091337059","display_name":"Jean\u2010Guillaume Dumas","orcid":"https://orcid.org/0000-0002-2591-172X"},"institutions":[{"id":"https://openalex.org/I4210149092","display_name":"Laboratoire Jean Kuntzmann","ror":"https://ror.org/04ett5b41","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I4210149092","https://openalex.org/I899635006","https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Jean-Guillaume Dumas","raw_affiliation_strings":["Laboratoire Jean Kuntzmann, Université Grenoble Alpes, France"],"affiliations":[{"raw_affiliation_string":"Laboratoire Jean Kuntzmann, Université Grenoble Alpes, France","institution_ids":["https://openalex.org/I4210149092"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079752845","display_name":"Cl\u00e9ment Pernet","orcid":"https://orcid.org/0000-0001-6970-0417"},"institutions":[{"id":"https://openalex.org/I4210149092","display_name":"Laboratoire Jean Kuntzmann","ror":"https://ror.org/04ett5b41","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I4210149092","https://openalex.org/I899635006","https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Cl\u00e9ment Pernet","raw_affiliation_strings":["Laboratoire Jean Kuntzmann, Université Grenoble Alpes, France"],"affiliations":[{"raw_affiliation_string":"Laboratoire Jean Kuntzmann, Université Grenoble Alpes, France","institution_ids":["https://openalex.org/I4210149092"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070868933","display_name":"Alexandre Sedoglavic","orcid":"https://orcid.org/0000-0003-3225-8631"},"institutions":[{"id":"https://openalex.org/I4210115519","display_name":"Centre de Recherche en Informatique","ror":"https://ror.org/020cdve92","country_code":"FR","type":"facility","lineage":["https://openalex.org/I190752583","https://openalex.org/I2746051580","https://openalex.org/I4210091621","https://openalex.org/I4210115519","https://openalex.org/I70768539"]},{"id":"https://openalex.org/I4387153239","display_name":"Centre de Recherche en Informatique, Signal et Automatique de Lille","ror":"https://ror.org/05vrs3189","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I2279609970","https://openalex.org/I4387153239","https://openalex.org/I7454413"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Alexandre Sedoglavic","raw_affiliation_strings":["Centre de Recherche en Informatique, Signal eT Automatique de Lille, Université de Lille, France"],"affiliations":[{"raw_affiliation_string":"Centre de Recherche en Informatique, Signal eT Automatique de Lille, Université de Lille, France","institution_ids":["https://openalex.org/I4210115519","https://openalex.org/I4387153239"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5091337059"],"corresponding_institution_ids":["https://openalex.org/I4210149092"],"apc_list":null,"apc_paid":null,"fwci":1.1141,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.70269453,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"254","last_page":"263"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9435999989509583,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9435999989509583,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":0.9225999712944031,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9197999835014343,"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":0.6774569153785706},{"id":"https://openalex.org/keywords/political-science","display_name":"Political science","score":0.5048390030860901},{"id":"https://openalex.org/keywords/library-science","display_name":"Library science","score":0.48421716690063477},{"id":"https://openalex.org/keywords/publics","display_name":"Publics","score":0.4737076461315155},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42497938871383667},{"id":"https://openalex.org/keywords/humanities","display_name":"Humanities","score":0.3970394432544708},{"id":"https://openalex.org/keywords/art","display_name":"Art","score":0.1646229326725006},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16043078899383545},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.09158620238304138}],"concepts":[{"id":"https://openalex.org/C39096654","wikidata":"https://www.wikidata.org/wiki/Q728507","display_name":"Strassen algorithm","level":4,"score":0.6774569153785706},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.5048390030860901},{"id":"https://openalex.org/C161191863","wikidata":"https://www.wikidata.org/wiki/Q199655","display_name":"Library science","level":1,"score":0.48421716690063477},{"id":"https://openalex.org/C2776663400","wikidata":"https://www.wikidata.org/wiki/Q7258081","display_name":"Publics","level":3,"score":0.4737076461315155},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42497938871383667},{"id":"https://openalex.org/C15708023","wikidata":"https://www.wikidata.org/wiki/Q80083","display_name":"Humanities","level":1,"score":0.3970394432544708},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.1646229326725006},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16043078899383545},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.09158620238304138},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"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/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1145/3666000.3669697","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3666000.3669697","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2024 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:2402.05630","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2402.05630","pdf_url":"https://arxiv.org/pdf/2402.05630","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:HAL:hal-04441653v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04441653","pdf_url":"https://hal.science/hal-04441653/document","source":{"id":"https://openalex.org/S4406922454","display_name":"SPIRE - Sciences Po Institutional REpository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"https://hal.science/hal-04441653","raw_type":"info:eu-repo/semantics/preprint"},{"id":"pmh:oai:HAL:hal-04927400v1","is_oa":false,"landing_page_url":"https://hal.science/hal-04927400","pdf_url":null,"source":{"id":"https://openalex.org/S4406922460","display_name":"SPIRE - Sciences Po Institutional REpository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2024, ⟨swh:1:dir:624e6f505f0152fd9553d24174af5e4ec5295e8f;origin=https://github.com/jgdumas/Fast-Matrix-Multiplication;visit=swh:1:snp:bf61e170ae54c4e16afc9f3ea3ac09beee525236;anchor=swh:1:rev:6c157fe290af96907c137762643b28da636e4a01⟩","raw_type":"Software"},{"id":"pmh:oai:lilloa.univ-lille.fr:20.500.12210/115697","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306402203","display_name":"LillOA (Universit\u00e9 de Lille (University Of Lille))","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210123514","host_organization_name":"Centre d'Etudes en Civilisations, Langues et Litt\u00e9ratures Etrang\u00e8res","host_organization_lineage":["https://openalex.org/I4210123514"],"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":null,"raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"doi:10.48550/arxiv.2402.05630","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2402.05630","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2402.05630","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2402.05630","pdf_url":"https://arxiv.org/pdf/2402.05630","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4391631734.pdf"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1539834906","https://openalex.org/W1983419392","https://openalex.org/W2003858108","https://openalex.org/W2011461657","https://openalex.org/W2020804487","https://openalex.org/W2031905258","https://openalex.org/W2035476608","https://openalex.org/W2060075517","https://openalex.org/W2073327480","https://openalex.org/W2096280747","https://openalex.org/W2110873104","https://openalex.org/W2147348850","https://openalex.org/W2493665548","https://openalex.org/W4388283233"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W4303646773","https://openalex.org/W2613375081","https://openalex.org/W2069906535","https://openalex.org/W2950769433","https://openalex.org/W2561887839","https://openalex.org/W2041189380","https://openalex.org/W1964529245"],"abstract_inverted_index":{"We":[0],"propose":[1],"a":[2,17,30,73,99],"non-commutative":[3],"algorithm":[4,14],"for":[5,90],"multiplying":[6],"2x2":[7],"matrices":[8],"using":[9],"7":[10],"coefficient":[11],"products.":[12],"This":[13],"reaches":[15],"simultaneously":[16],"better":[18],"accuracy":[19,61],"in":[20],"practice":[21],"compared":[22],"to":[23,97],"previously":[24],"known":[25,38],"such":[26],"fast":[27],"algorithms,":[28],"and":[29,53,60,122],"time":[31,119],"complexity":[32,120],"bound":[33],"with":[34],"the":[35,58,77,92,118,125],"best":[36],"currently":[37],"leading":[39],"term":[40],"(obtained":[41],"via":[42],"alternate":[43,112],"basis":[44,113],"sparsification).":[45],"To":[46],"build":[47],"this":[48],"algorithm,":[49],"we":[50,67,87,109],"consider":[51],"matrix":[52,64],"tensor":[54,84],"norms":[55],"bounds":[56,70],"governing":[57],"stability":[59],"of":[62,80,94],"numerical":[63],"multiplication.":[65],"First,":[66],"reduce":[68],"those":[69],"by":[71],"minimizing":[72,91],"growth":[74],"factor":[75],"along":[76],"unique":[78],"orbit":[79],"Strassen's":[81],"2x2-matrix":[82],"multiplication":[83],"decomposition.":[85],"Second,":[86],"develop":[88],"heuristics":[89],"number":[93],"operations":[95],"required":[96],"realize":[98],"given":[100],"bilinear":[101],"formula,":[102],"while":[103],"further":[104],"improving":[105],"its":[106],"accuracy.":[107,127],"Third,":[108],"perform":[110],"an":[111],"sparsification":[114],"that":[115],"improves":[116],"on":[117],"constant":[121],"mostly":[123],"preserves":[124],"overall":[126]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2024-02-08T00:00:00"}