{"id":"https://openalex.org/W2946108268","doi":"https://doi.org/10.1080/23799927.2020.1861104","title":"Randomization of approximate bilinear computation for matrix multiplication","display_name":"Randomization of approximate bilinear computation for matrix multiplication","publication_year":2020,"publication_date":"2020-12-14","ids":{"openalex":"https://openalex.org/W2946108268","doi":"https://doi.org/10.1080/23799927.2020.1861104","mag":"2946108268"},"language":"en","primary_location":{"id":"doi:10.1080/23799927.2020.1861104","is_oa":false,"landing_page_url":"https://doi.org/10.1080/23799927.2020.1861104","pdf_url":null,"source":{"id":"https://openalex.org/S4210234901","display_name":"International Journal of Computer Mathematics Computer Systems Theory","issn_l":"2379-9927","issn":["2379-9927","2379-9935"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics: Computer Systems Theory","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1905.07439","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062480532","display_name":"Osman Asif Malik","orcid":"https://orcid.org/0000-0003-4477-481X"},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Osman Asif Malik","raw_affiliation_strings":["Department of Applied Mathematics, University of Colorado Boulder, Boulder, CO, USA"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Colorado Boulder, Boulder, CO, USA","institution_ids":["https://openalex.org/I188538660"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086042756","display_name":"Stephen Becker","orcid":"https://orcid.org/0000-0002-1932-8159"},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Stephen Becker","raw_affiliation_strings":["Department of Applied Mathematics, University of Colorado Boulder, Boulder, CO, USA"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Colorado Boulder, Boulder, CO, USA","institution_ids":["https://openalex.org/I188538660"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5062480532"],"corresponding_institution_ids":["https://openalex.org/I188538660"],"apc_list":null,"apc_paid":null,"fwci":0.1443,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.48417045,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"6","issue":"1","first_page":"54","last_page":"93"},"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9986000061035156,"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":0.9970999956130981,"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/computation","display_name":"Computation","score":0.811416745185852},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.7329251766204834},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.6706173419952393},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.6470913887023926},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5415303111076355},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5361829400062561},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5171941518783569},{"id":"https://openalex.org/keywords/floating-point","display_name":"Floating point","score":0.4757651686668396},{"id":"https://openalex.org/keywords/numerical-linear-algebra","display_name":"Numerical linear algebra","score":0.42894014716148376},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.4260205030441284},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.39570939540863037},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.16447713971138},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.05981650948524475}],"concepts":[{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.811416745185852},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.7329251766204834},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.6706173419952393},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.6470913887023926},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5415303111076355},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5361829400062561},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5171941518783569},{"id":"https://openalex.org/C84211073","wikidata":"https://www.wikidata.org/wiki/Q117879","display_name":"Floating point","level":2,"score":0.4757651686668396},{"id":"https://openalex.org/C163834973","wikidata":"https://www.wikidata.org/wiki/Q2004891","display_name":"Numerical linear algebra","level":3,"score":0.42894014716148376},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4260205030441284},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39570939540863037},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.16447713971138},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.05981650948524475},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"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/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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/23799927.2020.1861104","is_oa":false,"landing_page_url":"https://doi.org/10.1080/23799927.2020.1861104","pdf_url":null,"source":{"id":"https://openalex.org/S4210234901","display_name":"International Journal of Computer Mathematics Computer Systems Theory","issn_l":"2379-9927","issn":["2379-9927","2379-9935"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics: Computer Systems Theory","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1905.07439","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1905.07439","pdf_url":"https://arxiv.org/pdf/1905.07439","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":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1905.07439","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1905.07439","pdf_url":"https://arxiv.org/pdf/1905.07439","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":null,"raw_type":"text"},"sustainable_development_goals":[{"score":0.44999998807907104,"id":"https://metadata.un.org/sdg/4","display_name":"Quality Education"}],"awards":[{"id":"https://openalex.org/G3282521955","display_name":null,"funder_award_id":"ECCS-1810314","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"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W1500468642","https://openalex.org/W1561337879","https://openalex.org/W1601946875","https://openalex.org/W1841592590","https://openalex.org/W1977662557","https://openalex.org/W1978106295","https://openalex.org/W1982842710","https://openalex.org/W1992111571","https://openalex.org/W1996440503","https://openalex.org/W2002048434","https://openalex.org/W2004916460","https://openalex.org/W2004948173","https://openalex.org/W2007211241","https://openalex.org/W2011461657","https://openalex.org/W2019603005","https://openalex.org/W2019865138","https://openalex.org/W2024440951","https://openalex.org/W2028087580","https://openalex.org/W2035476608","https://openalex.org/W2042465463","https://openalex.org/W2069537365","https://openalex.org/W2110873104","https://openalex.org/W2147348850","https://openalex.org/W2201600774","https://openalex.org/W2402512549","https://openalex.org/W2493665548","https://openalex.org/W2798909945","https://openalex.org/W2888024215","https://openalex.org/W2889797931","https://openalex.org/W2913731593","https://openalex.org/W2940563789","https://openalex.org/W2950034300","https://openalex.org/W2953235111","https://openalex.org/W2963374099","https://openalex.org/W3099472489","https://openalex.org/W4253527177","https://openalex.org/W4312258136","https://openalex.org/W6601968593"],"related_works":["https://openalex.org/W3099313426","https://openalex.org/W4287593139","https://openalex.org/W752783541","https://openalex.org/W1506547947","https://openalex.org/W4206811032","https://openalex.org/W2995605830","https://openalex.org/W2086123442","https://openalex.org/W2596457687","https://openalex.org/W3212757063","https://openalex.org/W2093666864"],"abstract_inverted_index":{"We":[0,24],"present":[1,109,117],"a":[2],"method":[3,98],"for":[4,7,59],"randomizing":[5],"formulas":[6,53],"bilinear":[8],"computation":[9,45],"of":[10,21,28,36,76,106],"matrix":[11,61],"products":[12],"which":[13],"does":[14],"not":[15],"increase":[16],"the":[17,22,26,44,103,119],"leading":[18],"order":[19],"complexity":[20],"computation.":[23],"consider":[25],"implications":[27],"such":[29],"randomization":[30],"when":[31,56,81,102,114],"there":[32],"are":[33,108,116],"two":[34,104],"sources":[35],"error.":[37],"The":[38,64],"first":[39],"source":[40,66],"is":[41,67,78],"due":[42,68],"to":[43,69],"formula":[46],"itself":[47],"only":[48],"being":[49],"approximately":[50],"correct.":[51],"Such":[52],"come":[54],"up":[55],"numerically":[57],"searching":[58],"faster":[60],"multiplication":[62],"algorithms.":[63],"second":[65],"using":[70],"floating":[71],"point":[72],"arithmetic.":[73],"This":[74],"kind":[75],"error":[77,107],"especially":[79],"important":[80],"computing":[82],"on":[83],"low":[84],"precision":[85],"hardware":[86],"like":[87],"GPUs.":[88],"Our":[89],"theoretical":[90],"results":[91],"and":[92],"numerical":[93],"experiments":[94],"indicate":[95],"that":[96],"our":[97],"can":[99],"improve":[100],"performance":[101],"kinds":[105],"individually,":[110],"as":[111,113],"well":[112],"they":[115],"at":[118],"same":[120],"time.":[121]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2019-05-29T00:00:00"}
