{"id":"https://openalex.org/W2121663287","doi":"https://doi.org/10.1109/sfcs.1975.14","title":"Fast parallel matrix inversion algorithms","display_name":"Fast parallel matrix inversion algorithms","publication_year":1975,"publication_date":"1975-10-01","ids":{"openalex":"https://openalex.org/W2121663287","doi":"https://doi.org/10.1109/sfcs.1975.14","mag":"2121663287"},"language":"en","primary_location":{"id":"doi:10.1109/sfcs.1975.14","doi":"https://doi.org/10.1109/sfcs.1975.14","is_oa":false,"landing_page_url":"https://doi.org/10.1109/sfcs.1975.14","pdf_url":null,"source":{"id":"https://openalex.org/S4210175768","display_name":"Annual Symposium on Foundations of Computer Science","issn_l":"0272-5428","issn":["0272-5428"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"16th Annual Symposium on Foundations of Computer Science (sfcs 1975)","raw_type":"proceedings-article"},"volume":null,"type":"conference-paper","is_traditional":true,"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/A5010390853","display_name":"L. Csanky","orcid":null,"observed_orcids":[]},"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":"L. Csanky","raw_affiliation_strings":["Computer Science Division Department of Electrical Engineering and Computer Sciences and the Electronics Research Laboratory, University of California Berkeley, Berkeley, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science Division Department of Electrical Engineering and Computer Sciences and the Electronics Research Laboratory, University of California Berkeley, Berkeley, CA, USA","institution_ids":["https://openalex.org/I95457486"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5010390853"],"corresponding_institution_ids":["https://openalex.org/I95457486"],"apc_list":null,"apc_paid":null,"fwci":4.7155,"has_fulltext":false,"cited_by_count":50,"citation_normalized_percentile":{"value":0.96573209,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"11","last_page":"12"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.4717000126838684,"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":0.4717000126838684,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.4438000023365021,"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":0.0551999993622303,"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/linear-systems-of-equations","display_name":"systems of linear equations","score":0.824999988079071},{"id":"https://openalex.org/keywords/matrix-determinant-computation","display_name":"matrix determinant computation","score":0.6549999713897705},{"id":"https://openalex.org/keywords/characteristic-polynomial","display_name":"characteristic polynomial","score":0.8169999718666077},{"id":"https://openalex.org/keywords/lower-bounds","display_name":"lower bounds","score":0.625}],"concepts":[{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6183603405952454},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5681493282318115},{"id":"https://openalex.org/C120373497","wikidata":"https://www.wikidata.org/wiki/Q1087987","display_name":"Parallel algorithm","level":2,"score":0.5176806449890137},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5139562487602234},{"id":"https://openalex.org/C1893757","wikidata":"https://www.wikidata.org/wiki/Q3653001","display_name":"Inversion (geology)","level":3,"score":0.490700364112854},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.48859649896621704},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.4877846837043762},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.4823581576347351},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.46473264694213867},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4586307108402252},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.45120561122894287},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.4417005181312561},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.43367812037467957},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.383640855550766},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3747381865978241},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3347073197364807},{"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/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},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/sfcs.1975.14","doi":"https://doi.org/10.1109/sfcs.1975.14","is_oa":false,"landing_page_url":"https://doi.org/10.1109/sfcs.1975.14","pdf_url":null,"source":{"id":"https://openalex.org/S4210175768","display_name":"Annual Symposium on Foundations of Computer Science","issn_l":"0272-5428","issn":["0272-5428"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"16th Annual Symposium on Foundations of Computer Science (sfcs 1975)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":1,"referenced_works":["https://openalex.org/W2319624714"],"related_works":["https://openalex.org/W2107822913","https://openalex.org/W1995272909","https://openalex.org/W46767947","https://openalex.org/W1510646708","https://openalex.org/W2072582972","https://openalex.org/W7214721405","https://openalex.org/W2027333436","https://openalex.org/W2393029629","https://openalex.org/W2120762604","https://openalex.org/W2171640788"],"abstract_inverted_index":{"In":[0],"this":[1,77,147],"paper,":[2],"an":[3,39,109],"investigation":[4],"of":[5,10,15,25,34,50,62,80,97,132,152],"the":[6,22,48,51,60,66,93,103,125,128,143],"parallel":[7,31,94,129],"arithmetic":[8,32,95,130],"complexity":[9,33,49,96,131],"matrix":[11,27],"inversion,":[12],"solving":[13,35],"systems":[14],"linear":[16],"equations,":[17],"computing":[18,21],"determinants":[19],"and":[20,65,107,142],"characteristic":[23],"polynomial":[24,154],"a":[26,150],"is":[28,59,137],"reported.":[29],"The":[30,45,85],"equations":[36],"has":[37,102],"been":[38],"open":[40],"question":[41],"for":[42],"several":[43],"years.":[44],"gap":[46],"between":[47],"best":[52],"algorithms":[53,144],"(2n":[54],"+":[55],"0(1),":[56],"where":[57],"n":[58,73],"number":[61,151],"unknowns/":[63],"equations)":[64],"only":[67],"proved":[68],"lower":[69],"bound":[70,148],"(2":[71],"log":[72],"(All":[74],"logarithms":[75],"in":[76,115,124,155],"paper":[78],"are":[79],"base":[81],"two.))":[82],"was":[83],"huge.":[84],"first":[86],"breakthrough":[87],"came":[88],"when":[89],"Csanky":[90],"reported":[91],"that":[92,111,127,145],"all":[98,133],"these":[99,113,134],"four":[100,135],"problems":[101,114,136],"same":[104],"growth":[105],"rate":[106],"exhibited":[108],"algorithm":[110],"computes":[112],"2n":[116],"-":[117],"O(log2n)":[118,141],"steps.":[119],"It":[120],"will":[121],"be":[122],"shown":[123],"sequel":[126],"upper":[138],"bounded":[139],"by":[140],"establish":[146],"use":[149],"processors":[153],"n.":[156],"This":[157],"disproves":[158],"I.":[159],"Munro's":[160],"conjecture.":[161]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2016-06-24T00:00:00"}
