{"id":"https://openalex.org/W2077741232","doi":"https://doi.org/10.1145/2755996.2756672","title":"A Relaxed Algorithm for Online Matrix Inversion","display_name":"A Relaxed Algorithm for Online Matrix Inversion","publication_year":2015,"publication_date":"2015-06-24","ids":{"openalex":"https://openalex.org/W2077741232","doi":"https://doi.org/10.1145/2755996.2756672","mag":"2077741232"},"language":"en","primary_location":{"id":"doi:10.1145/2755996.2756672","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2755996.2756672","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008351804","display_name":"Arne Storjohann","orcid":"https://orcid.org/0000-0002-6354-8810"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Arne Storjohann","raw_affiliation_strings":["University of Waterloo, Waterloo, ON, Canada"],"affiliations":[{"raw_affiliation_string":"University of Waterloo, Waterloo, ON, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073160650","display_name":"Shiyun Yang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shiyun Yang","raw_affiliation_strings":["Amazon Canada Fullfuillment Services Inc, Vancouver, BC, Canada"],"affiliations":[{"raw_affiliation_string":"Amazon Canada Fullfuillment Services Inc, Vancouver, BC, Canada","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5008351804"],"corresponding_institution_ids":["https://openalex.org/I151746483"],"apc_list":null,"apc_paid":null,"fwci":1.30155663,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.84065918,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"339","last_page":"346"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9983000159263611,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9983000159263611,"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":0.9976999759674072,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9970999956130981,"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/invertible-matrix","display_name":"Invertible matrix","score":0.7927433252334595},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6566593647003174},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5593617558479309},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5532401204109192},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.5411692261695862},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5401808619499207},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5294358730316162},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5217707753181458},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.49848461151123047},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.48612499237060547},{"id":"https://openalex.org/keywords/inversion","display_name":"Inversion (geology)","score":0.44643154740333557},{"id":"https://openalex.org/keywords/row","display_name":"Row","score":0.44263508915901184},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.41460925340652466},{"id":"https://openalex.org/keywords/row-and-column-spaces","display_name":"Row and column spaces","score":0.41373735666275024},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.377533495426178},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.15737244486808777},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.09657138586044312}],"concepts":[{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.7927433252334595},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6566593647003174},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5593617558479309},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5532401204109192},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.5411692261695862},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5401808619499207},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5294358730316162},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5217707753181458},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.49848461151123047},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.48612499237060547},{"id":"https://openalex.org/C1893757","wikidata":"https://www.wikidata.org/wiki/Q3653001","display_name":"Inversion (geology)","level":3,"score":0.44643154740333557},{"id":"https://openalex.org/C135598885","wikidata":"https://www.wikidata.org/wiki/Q1366302","display_name":"Row","level":2,"score":0.44263508915901184},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.41460925340652466},{"id":"https://openalex.org/C104140500","wikidata":"https://www.wikidata.org/wiki/Q2088159","display_name":"Row and column spaces","level":3,"score":0.41373735666275024},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.377533495426178},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.15737244486808777},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.09657138586044312},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0},{"id":"https://openalex.org/C109007969","wikidata":"https://www.wikidata.org/wiki/Q749565","display_name":"Structural basin","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/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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":1,"locations":[{"id":"doi:10.1145/2755996.2756672","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2755996.2756672","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1502124338","https://openalex.org/W1991713476","https://openalex.org/W2004895252","https://openalex.org/W2015497178","https://openalex.org/W2029504359","https://openalex.org/W2053637543","https://openalex.org/W2060801388","https://openalex.org/W2072487213","https://openalex.org/W2082180697","https://openalex.org/W2085819076","https://openalex.org/W2113203238","https://openalex.org/W2281479637","https://openalex.org/W2327732228","https://openalex.org/W4302081240","https://openalex.org/W6608815102","https://openalex.org/W6701493093"],"related_works":["https://openalex.org/W2313440505","https://openalex.org/W3123744736","https://openalex.org/W2137691148","https://openalex.org/W1505848319","https://openalex.org/W4281399881","https://openalex.org/W2905020035","https://openalex.org/W3166006430","https://openalex.org/W4281971614","https://openalex.org/W2049180840","https://openalex.org/W1992086467"],"abstract_inverted_index":{"We":[0,99],"consider":[1],"a":[2,15,24,73,111,131],"variation":[3,28],"of":[4,9,19,64,115,124],"the":[5,11,42,53,62,65,83,88,91,122,135,165,177],"well":[6],"known":[7],"problem":[8,102],"computing":[10],"unique":[12],"solution":[13,44,54,89],"to":[14,55,77,90,140,149,159],"nonsingular":[16],"system":[17,67],"Ax=b":[18],"n":[20],"linear":[21],"equations":[22],"over":[23],"field":[25,116],"K.":[26],"The":[27,104],"assumes":[29],"that":[30,118,146],"A":[31],"has":[32,110],"generic":[33],"rank":[34,171],"profile":[35,172],"and":[36,79,137],"requires":[37],"as":[38,80,82],"output":[39],"not":[40],"only":[41],"single":[43],"vector":[45],"A-1b":[46],"\u0395":[47],"Kn":[48],"x":[49],"1,":[50],"but":[51],"rather":[52],"all":[56],"leading":[57,93],"principle":[58],"subsystems.":[59],"Most":[60],"importantly,":[61],"rows":[63],"augmented":[66],"[A||b]":[68],"are":[69],"given":[70,87],"one":[71],"at":[72],"time":[74],"from":[75],"first":[76],"last,":[78],"soon":[81],"next":[84,92],"row":[85,170],"is":[86,119],"principal":[94],"subsystem":[95],"should":[96],"be":[97],"produced.":[98],"call":[100],"this":[101,127],"ONLINESYSTEM.":[103],"obvious":[105],"iterative":[106,167],"algorithm":[107,143,168],"for":[108,134,144,169],"ONLINESYSTEM":[109,145],"cost":[112],"in":[113,121],"terms":[114],"operations":[117],"cubic":[120],"dimension":[123],"A.":[125],"In":[126],"paper":[128],"we":[129,156],"introduce":[130,160],"relaxed":[132],"representation":[133],"inverse":[136],"show":[138,157],"how":[139,158],"obtain":[141],"an":[142,154],"allows":[147],"us":[148],"incorporate":[150],"matrix":[151,162],"multiplication.":[152],"As":[153],"application":[155],"fast":[161],"multiplication":[163],"into":[164],"inherently":[166],"computation":[173],"presented":[174],"previously":[175],"by":[176],"authors.":[178]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
