{"id":"https://openalex.org/W2147348850","doi":"https://doi.org/10.1007/s00211-007-0061-6","title":"Fast matrix multiplication is stable","display_name":"Fast matrix multiplication is stable","publication_year":2007,"publication_date":"2007-02-08","ids":{"openalex":"https://openalex.org/W2147348850","doi":"https://doi.org/10.1007/s00211-007-0061-6","mag":"2147348850"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-007-0061-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-007-0061-6","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/math/0603207","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076825233","display_name":"James Demmel","orcid":"https://orcid.org/0000-0003-1145-3745"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"James Demmel","raw_affiliation_strings":["Computer Science Division, University of California, Berkeley, CA, 94720, USA","Mathematics Department, University of California, Berkeley, CA, 94720, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science Division, University of California, Berkeley, CA, 94720, USA","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"Mathematics Department, University of California, Berkeley, CA, 94720, USA","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031997473","display_name":"Ioana Dumitriu","orcid":null},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ioana Dumitriu","raw_affiliation_strings":["Mathematics Department, University of California, Berkeley, CA, 94720, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department, University of California, Berkeley, CA, 94720, USA","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055605632","display_name":"Olga Holtz","orcid":"https://orcid.org/0000-0003-3420-3423"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Olga Holtz","raw_affiliation_strings":["Mathematics Department, University of California, Berkeley, CA, 94720, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department, University of California, Berkeley, CA, 94720, USA","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040052580","display_name":"Robert Kleinberg","orcid":"https://orcid.org/0000-0002-8306-3407"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Robert Kleinberg","raw_affiliation_strings":["Computer Science Division, University of California, Berkeley, CA, 94720, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science Division, University of California, Berkeley, CA, 94720, USA","institution_ids":["https://openalex.org/I95457486"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5055605632"],"corresponding_institution_ids":["https://openalex.org/I95457486"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":2.2295,"has_fulltext":true,"cited_by_count":79,"citation_normalized_percentile":{"value":0.88356754,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"106","issue":"2","first_page":"199","last_page":"224"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9980000257492065,"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":0.9980000257492065,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9950000047683716,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9919999837875366,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/multiplication","display_name":"Multiplication (music)","score":0.8128176927566528},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.6971365213394165},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6235266327857971},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.5866812467575073},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5741145014762878},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5531951189041138},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5341934561729431},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5147271156311035},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.4527778923511505},{"id":"https://openalex.org/keywords/error-analysis","display_name":"Error analysis","score":0.417377233505249},{"id":"https://openalex.org/keywords/multiplication-algorithm","display_name":"Multiplication algorithm","score":0.4108959436416626},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3526403605937958},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.33199626207351685},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.30250057578086853},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.18985339999198914},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.17376333475112915},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10385197401046753}],"concepts":[{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.8128176927566528},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.6971365213394165},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6235266327857971},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.5866812467575073},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5741145014762878},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5531951189041138},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5341934561729431},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5147271156311035},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4527778923511505},{"id":"https://openalex.org/C3018824978","wikidata":"https://www.wikidata.org/wiki/Q2894891","display_name":"Error analysis","level":2,"score":0.417377233505249},{"id":"https://openalex.org/C201290732","wikidata":"https://www.wikidata.org/wiki/Q130762","display_name":"Multiplication algorithm","level":3,"score":0.4108959436416626},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3526403605937958},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33199626207351685},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30250057578086853},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.18985339999198914},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.17376333475112915},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10385197401046753},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"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/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":8,"locations":[{"id":"doi:10.1007/s00211-007-0061-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-007-0061-6","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:math/0603207","is_oa":true,"landing_page_url":"https://arxiv.org/abs/math/0603207","pdf_url":"https://arxiv.org/pdf/math/0603207","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.236.1134","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.236.1134","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0603207v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.236.4122","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.236.4122","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0603207v2.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.236.7185","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.236.7185","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0603207v3.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.98.3909","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.98.3909","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.washington.edu/~dumitriu/matmul_xiv.pdf","raw_type":"text"},{"id":"pmh:oai:escholarship.org/ark:/13030/qt03v4r4qh","is_oa":false,"landing_page_url":"https://escholarship.org/uc/item/03v4r4qh","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Numerische Mathematik, vol 106, iss 2","raw_type":"article"},{"id":"pmh:qt03v4r4qh","is_oa":false,"landing_page_url":"http://www.escholarship.org/uc/item/03v4r4qh","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Demmel, James; Holtz, Olga; Kleinberg, Robert; &amp; Dumitriu, Ioana. (2007). Fast matrix multiplication is stable. Numerische Mathematik, 106(2), 199 - 224. doi: 10.1007/s00211-007-0061-6. UC Berkeley: Retrieved from: http://www.escholarship.org/uc/item/03v4r4qh","raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:math/0603207","is_oa":true,"landing_page_url":"https://arxiv.org/abs/math/0603207","pdf_url":"https://arxiv.org/pdf/math/0603207","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1520514311","display_name":"TERASCALE OPTIMAL BDE         SIMULATIONS (TOPS) CENTER","funder_award_id":"FC02-01ER25478","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G7766933102","display_name":"ITR/NGS: Automatic Performance Tuning for Large Scale Scientific Applications","funder_award_id":"0325873","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7823918874","display_name":"Reliable and Scalable Software for Linear Algebra Computations on High End Computers","funder_award_id":"0444486","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320309634","display_name":"Adolph C. and Mary Sprague Miller Institute for Basic Research in Science, University of California Berkeley","ror":null},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W94439627","https://openalex.org/W1480928214","https://openalex.org/W1561337879","https://openalex.org/W1578920057","https://openalex.org/W1601946875","https://openalex.org/W1968408352","https://openalex.org/W1979740015","https://openalex.org/W1984797285","https://openalex.org/W2010537260","https://openalex.org/W2011461657","https://openalex.org/W2020804487","https://openalex.org/W2035476608","https://openalex.org/W2061397794","https://openalex.org/W2083368929","https://openalex.org/W2110873104","https://openalex.org/W2111612671","https://openalex.org/W2125457238","https://openalex.org/W2153063335","https://openalex.org/W2890534020","https://openalex.org/W3022909171","https://openalex.org/W3099443264","https://openalex.org/W3099472489","https://openalex.org/W3149756008","https://openalex.org/W4229666556","https://openalex.org/W4231150350","https://openalex.org/W6634682466"],"related_works":["https://openalex.org/W2225983048","https://openalex.org/W2372139915","https://openalex.org/W2596457687","https://openalex.org/W3099313426","https://openalex.org/W752783541","https://openalex.org/W4287593139","https://openalex.org/W1516189266","https://openalex.org/W2093666864","https://openalex.org/W4378602953","https://openalex.org/W4312443197"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":9}],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2025-10-10T00:00:00"}
