{"id":"https://openalex.org/W4387964245","doi":"https://doi.org/10.1145/3666000.3669671","title":"In-place accumulation of fast multiplication formulae","display_name":"In-place accumulation of fast multiplication formulae","publication_year":2024,"publication_date":"2024-07-15","ids":{"openalex":"https://openalex.org/W4387964245","doi":"https://doi.org/10.1145/3666000.3669671"},"language":"en","primary_location":{"id":"doi:10.1145/3666000.3669671","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3666000.3669671","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":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-04167499v4/document","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"]},{"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":true,"raw_author_name":"Jean-Guillaume Dumas","raw_affiliation_strings":["Laboratoire Jean Kuntzmann, Universit\u00e9 Grenoble Alpes, France"],"affiliations":[{"raw_affiliation_string":"Laboratoire Jean Kuntzmann, Universit\u00e9 Grenoble Alpes, France","institution_ids":["https://openalex.org/I4210149092","https://openalex.org/I899635006"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003590565","display_name":"Bruno Grenet","orcid":"https://orcid.org/0000-0003-2057-5429"},"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"]},{"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":"Bruno Grenet","raw_affiliation_strings":["Laboratoire Jean Kuntzmann, Universit\u00e9 Grenoble Alpes, France"],"affiliations":[{"raw_affiliation_string":"Laboratoire Jean Kuntzmann, Universit\u00e9 Grenoble Alpes, France","institution_ids":["https://openalex.org/I4210149092","https://openalex.org/I899635006"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5091337059"],"corresponding_institution_ids":["https://openalex.org/I4210149092","https://openalex.org/I899635006"],"apc_list":null,"apc_paid":null,"fwci":0.3617,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.55615173,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"16","last_page":"25"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9995999932289124,"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"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9990000128746033,"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"}},{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9990000128746033,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/strassen-algorithm","display_name":"Strassen algorithm","score":0.932598352432251},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.7720216512680054},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.7610085010528564},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5640740990638733},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5476691722869873},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.483636736869812},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4607928395271301},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45358067750930786},{"id":"https://openalex.org/keywords/multiplication-algorithm","display_name":"Multiplication algorithm","score":0.43212470412254333},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4303285479545593},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4224846363067627},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4039975702762604},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.36875659227371216},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.20320230722427368}],"concepts":[{"id":"https://openalex.org/C39096654","wikidata":"https://www.wikidata.org/wiki/Q728507","display_name":"Strassen algorithm","level":4,"score":0.932598352432251},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.7720216512680054},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.7610085010528564},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5640740990638733},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5476691722869873},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.483636736869812},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4607928395271301},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45358067750930786},{"id":"https://openalex.org/C201290732","wikidata":"https://www.wikidata.org/wiki/Q130762","display_name":"Multiplication algorithm","level":3,"score":0.43212470412254333},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4303285479545593},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4224846363067627},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4039975702762604},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.36875659227371216},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.20320230722427368},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1145/3666000.3669671","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3666000.3669671","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:HAL:hal-04167499v4","is_oa":true,"landing_page_url":"https://hal.science/hal-04167499","pdf_url":"https://hal.science/hal-04167499v4/document","source":{"id":"https://openalex.org/S4406922461","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":"Proceedings of the 49th International Symposium on Symbolic and Algebraic Computation (ISSAC'24), ACM SIGSAM, Jul 2024, Raleigh, NC, United States. pp.16-25, &#x27E8;10.1145/3666000.3669671&#x27E9;","raw_type":"Conference papers"},{"id":"pmh:oai:HAL:hal-04927443v1","is_oa":false,"landing_page_url":"https://hal.science/hal-04927443","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, &#x27E8;swh:1:dir:606e4719f7b82eea0bfd1dfc88d8beb9a666774e;origin=https://github.com/jgdumas/plinopt;visit=swh:1:snp:8f8eba5195a71803e3620f352e6b815e62f268fc;anchor=swh:1:rev:c6b63fa5cfa8aada9f5d6655621ba1b1fbf12588&#x27E9;","raw_type":"Software"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-04167499v4","is_oa":true,"landing_page_url":"https://hal.science/hal-04167499","pdf_url":"https://hal.science/hal-04167499v4/document","source":{"id":"https://openalex.org/S4406922461","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":"Proceedings of the 49th International Symposium on Symbolic and Algebraic Computation (ISSAC'24), ACM SIGSAM, Jul 2024, Raleigh, NC, United States. pp.16-25, &#x27E8;10.1145/3666000.3669671&#x27E9;","raw_type":"Conference papers"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4387964245.pdf"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W1582291092","https://openalex.org/W1983419392","https://openalex.org/W1998927407","https://openalex.org/W2004916460","https://openalex.org/W2024016477","https://openalex.org/W2035476608","https://openalex.org/W2053839977","https://openalex.org/W2055957023","https://openalex.org/W2061171222","https://openalex.org/W2065815779","https://openalex.org/W2069906535","https://openalex.org/W2083368929","https://openalex.org/W2104070031","https://openalex.org/W2112683629","https://openalex.org/W2121228963","https://openalex.org/W2145889866","https://openalex.org/W2169633255","https://openalex.org/W2918410320","https://openalex.org/W3003840168","https://openalex.org/W3009870468","https://openalex.org/W3120503253","https://openalex.org/W3208487748","https://openalex.org/W4288080171"],"related_works":["https://openalex.org/W2170716619","https://openalex.org/W2145889866","https://openalex.org/W2949595835","https://openalex.org/W2392656174","https://openalex.org/W3204033665","https://openalex.org/W2613375081","https://openalex.org/W4301181185","https://openalex.org/W2269364368","https://openalex.org/W2032839380","https://openalex.org/W1809313304"],"abstract_inverted_index":{"This":[0,146],"paper":[1],"deals":[2],"with":[3,55,71],"simultaneously":[4],"fast":[5,56,92,158],"and":[6,93,105,108,161],"in-place":[7,35,53,94,126,154],"algorithms":[8,96,156],"for":[9,97,103,157,162],"formulae":[10,100],"where":[11],"the":[12,34,62,73,125],"result":[13],"has":[14],"to":[15,51,80,112,128,132,141,151],"be":[16],"linearly":[17],"accumulated:":[18],"some":[19],"output":[20,74],"variables":[21,75],"are":[22,76,139],"also":[23],"input":[24],"variables,":[25],"linked":[26],"by":[27],"a":[28,87,117],"linear":[29,114],"dependency.":[30],"Fundamental":[31],"examples":[32],"include":[33],"accumulated":[36],"multiplication":[37],"of":[38,64,91,116,119],"polynomials":[39],"or":[40],"matrices,":[41],"<Formula":[42],"format=\"inline\"><TexMath><?TeX":[43],"$C\\operatorname{\\,{+}=\\,}{AB}$?></TexMath><AltText>Math":[44],"1</AltText><File":[45],"name=\"issac24-1-inline1\"":[46],"type=\"svg\"/></Formula>.":[47],"The":[48],"difficulty":[49],"is":[50],"combine":[52],"computations":[54],"algorithms:":[57],"those":[58,138],"usually":[59],"come":[60],"at":[61],"expense":[63],"(potentially":[65],"large)":[66],"extra":[67],"temporary":[68],"space,":[69],"but":[70],"accumulation":[72,115],"not":[77],"even":[78],"available":[79],"store":[81],"intermediate":[82],"values.":[83],"We":[84],"first":[85],"propose":[86],"novel":[88],"automatic":[89],"design":[90],"accumulating":[95,155],"any":[98,113,129],"bilinear":[99],"(and":[101],"thus":[102],"polynomial":[104,159],"matrix":[106,164],"multiplication)":[107],"then":[109],"extend":[110],"it":[111],"collection":[118],"functions.":[120],"For":[121],"this,":[122],"we":[123],"relax":[124],"model":[127],"algorithm":[130],"allowed":[131],"modify":[133],"its":[134],"inputs,":[135],"provided":[136],"that":[137],"restored":[140],"their":[142],"initial":[143],"state":[144],"afterwards.":[145],"allows":[147],"us,":[148],"in":[149],"fine,":[150],"derive":[152],"unprecedented":[153],"multiplications":[160],"Strassen-like":[163],"multiplications.":[165]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}