{"id":"https://openalex.org/W2020777648","doi":"https://doi.org/10.1155/1995/636457","title":"A Tensor Product Formulation of Strassen\u2032s Matrix Multiplication Algorithm with Memory Reduction","display_name":"A Tensor Product Formulation of Strassen\u2032s Matrix Multiplication Algorithm with Memory Reduction","publication_year":1995,"publication_date":"1995-01-01","ids":{"openalex":"https://openalex.org/W2020777648","doi":"https://doi.org/10.1155/1995/636457","mag":"2020777648"},"language":"en","primary_location":{"id":"doi:10.1155/1995/636457","is_oa":true,"landing_page_url":"https://doi.org/10.1155/1995/636457","pdf_url":"https://downloads.hindawi.com/journals/sp/1995/636457.pdf","source":{"id":"https://openalex.org/S166774750","display_name":"Scientific Programming","issn_l":"1058-9244","issn":["1058-9244","1875-919X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scientific Programming","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://downloads.hindawi.com/journals/sp/1995/636457.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088007800","display_name":"B. Raghu Kumar","orcid":"https://orcid.org/0000-0002-5147-624X"},"institutions":[{"id":"https://openalex.org/I52357470","display_name":"The Ohio State University","ror":"https://ror.org/00rs6vg23","country_code":"US","type":"education","lineage":["https://openalex.org/I52357470"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"B. Kumar","raw_affiliation_strings":["Department of Computer and Information Science, The Ohio State University, Columbus, OH 43210-1277, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer and Information Science, The Ohio State University, Columbus, OH 43210-1277, USA","institution_ids":["https://openalex.org/I52357470"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056626970","display_name":"Chien\u2010Hung Huang","orcid":"https://orcid.org/0000-0003-3905-8915"},"institutions":[{"id":"https://openalex.org/I52357470","display_name":"The Ohio State University","ror":"https://ror.org/00rs6vg23","country_code":"US","type":"education","lineage":["https://openalex.org/I52357470"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"C.-H. Huang","raw_affiliation_strings":["Department of Computer and Information Science, The Ohio State University, Columbus, OH 43210-1277, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer and Information Science, The Ohio State University, Columbus, OH 43210-1277, USA","institution_ids":["https://openalex.org/I52357470"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027517817","display_name":"P. Sadayappan","orcid":"https://orcid.org/0000-0002-4737-2034"},"institutions":[{"id":"https://openalex.org/I52357470","display_name":"The Ohio State University","ror":"https://ror.org/00rs6vg23","country_code":"US","type":"education","lineage":["https://openalex.org/I52357470"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"P. Sadayappan","raw_affiliation_strings":["Department of Computer and Information Science, The Ohio State University, Columbus, OH 43210-1277, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer and Information Science, The Ohio State University, Columbus, OH 43210-1277, USA","institution_ids":["https://openalex.org/I52357470"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103408440","display_name":"R. W. Johnson","orcid":null},"institutions":[{"id":"https://openalex.org/I173963315","display_name":"St. Cloud State University","ror":"https://ror.org/016czhx14","country_code":"US","type":"education","lineage":["https://openalex.org/I173963315","https://openalex.org/I91221267"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"R.W. Johnson","raw_affiliation_strings":["Department of Computer Science, St. Cloud State University, St. Cloud, MN 56301, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, St. Cloud State University, St. Cloud, MN 56301, USA","institution_ids":["https://openalex.org/I173963315"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1800,"currency":"USD","value_usd":1800},"apc_paid":{"value":1800,"currency":"USD","value_usd":1800},"fwci":0.0,"has_fulltext":true,"cited_by_count":18,"citation_normalized_percentile":{"value":0.12685381,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"4","issue":"4","first_page":"275","last_page":"289"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9993000030517578,"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":0.9993000030517578,"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":0.9933000206947327,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9775000214576721,"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":0.9968039989471436},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.8477843403816223},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5689166188240051},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.5338655114173889},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.5335650444030762},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.5268698334693909},{"id":"https://openalex.org/keywords/tensor-product","display_name":"Tensor product","score":0.5256142020225525},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4969768822193146},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.4888705611228943},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.47976455092430115},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.33306920528411865},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.12782633304595947},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.0925413966178894}],"concepts":[{"id":"https://openalex.org/C39096654","wikidata":"https://www.wikidata.org/wiki/Q728507","display_name":"Strassen algorithm","level":4,"score":0.9968039989471436},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.8477843403816223},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5689166188240051},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.5338655114173889},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.5335650444030762},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.5268698334693909},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.5256142020225525},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4969768822193146},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.4888705611228943},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.47976455092430115},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33306920528411865},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.12782633304595947},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0925413966178894},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/1995/636457","is_oa":true,"landing_page_url":"https://doi.org/10.1155/1995/636457","pdf_url":"https://downloads.hindawi.com/journals/sp/1995/636457.pdf","source":{"id":"https://openalex.org/S166774750","display_name":"Scientific Programming","issn_l":"1058-9244","issn":["1058-9244","1875-919X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scientific Programming","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:ec23c48fdcfb496cb79bd1c987afd46a","is_oa":false,"landing_page_url":"https://doaj.org/article/ec23c48fdcfb496cb79bd1c987afd46a","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"Scientific Programming, Vol 4, Iss 4, Pp 275-289 (1995)","raw_type":"article"},{"id":"pmh:oai:osti.gov:1198030","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/1198030","pdf_url":null,"source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"doi:10.1155/1995/636457","is_oa":true,"landing_page_url":"https://doi.org/10.1155/1995/636457","pdf_url":"https://downloads.hindawi.com/journals/sp/1995/636457.pdf","source":{"id":"https://openalex.org/S166774750","display_name":"Scientific Programming","issn_l":"1058-9244","issn":["1058-9244","1875-919X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scientific Programming","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/9","display_name":"Industry, innovation and infrastructure","score":0.44999998807907104}],"awards":[],"funders":[{"id":"https://openalex.org/F4320332178","display_name":"National Institute of Standards and Technology","ror":"https://ror.org/05xpvk416"},{"id":"https://openalex.org/F4320332276","display_name":"Advanced Research Projects Agency - Energy","ror":"https://ror.org/03q1rgc19"},{"id":"https://openalex.org/F4320332815","display_name":"Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2020777648.pdf","grobid_xml":"https://content.openalex.org/works/W2020777648.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W177749522","https://openalex.org/W1601946875","https://openalex.org/W1829171354","https://openalex.org/W1970548269","https://openalex.org/W1972907356","https://openalex.org/W1979005107","https://openalex.org/W2095590702","https://openalex.org/W2125457238","https://openalex.org/W2796941408","https://openalex.org/W6642874868"],"related_works":["https://openalex.org/W1974407206","https://openalex.org/W1829171354","https://openalex.org/W2004916460","https://openalex.org/W2962985479","https://openalex.org/W1523285705","https://openalex.org/W2772956802","https://openalex.org/W2804080973","https://openalex.org/W2613375081","https://openalex.org/W2056120647","https://openalex.org/W2069906535"],"abstract_inverted_index":{"In":[0,23,65],"this":[1,24,66],"article,":[2,67],"we":[3,68],"present":[4,69,114],"a":[5,15,70,115,140,147],"program":[6],"generation":[7],"strategy":[8],"of":[9,73,89,100],"Strassen\u2032s":[10,36,74,90],"matrix":[11,37,50],"multiplication":[12,38],"algorithm":[13,39,75,91],"using":[14],"programming":[16],"methodology":[17],"based":[18],"on":[19,139,146],"tensor":[20,46,94],"product":[21,95],"formulas.":[22],"methodology,":[25],"block":[26],"recursive":[27],"programs":[28],"such":[29,81],"as":[30,42,82],"the":[31,83,120],"fast":[32],"Fourier":[33],"Transforms":[34],"and":[35,48],"are":[40,150],"expressed":[41],"algebraic":[43],"formulas":[44,53,96],"involving":[45],"products":[47],"other":[49],"operations.":[51],"Such":[52],"can":[54],"be":[55],"systematically":[56],"translated":[57],"to":[58,126],"high\u2010performance":[59],"parallel/vector":[60],"codes":[61],"for":[62,76,105,136],"various":[63],"architectures.":[64],"nonrecursive":[71],"implementation":[72,88,138],"shared":[77,141],"memory":[78,142],"vector":[79],"processors":[80],"Cray":[84,148],"Y\u2010MP.":[85],"A":[86],"previous":[87],"synthesized":[92],"from":[93],"required":[97],"working":[98,121],"storage":[99,122],"size":[101],"O(7":[102],"n":[103,108,111,128],")":[104],"multiplying":[106],"2":[107,110],"\u00d7":[109],"matrices.":[112],"We":[113],"modified":[116,131],"formulation":[117,132],"in":[118],"which":[119],"requirement":[123],"is":[124],"reduced":[125],"O(4":[127],").":[129],"The":[130],"exhibits":[133],"sufficient":[134],"parallelism":[135],"efficient":[137],"multiprocessor.":[143],"Performance":[144],"results":[145],"Y\u2010MP8/64":[149],"presented.":[151]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}