{"id":"https://openalex.org/W2163688235","doi":"https://doi.org/10.1137/100788926","title":"CALU: A Communication Optimal LU Factorization Algorithm","display_name":"CALU: A Communication Optimal LU Factorization Algorithm","publication_year":2011,"publication_date":"2011-10-01","ids":{"openalex":"https://openalex.org/W2163688235","doi":"https://doi.org/10.1137/100788926","mag":"2163688235"},"language":"en","primary_location":{"id":"doi:10.1137/100788926","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100788926","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-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/A5040521001","display_name":"Laura Grigori","orcid":"https://orcid.org/0000-0002-5880-1076"},"institutions":[{"id":"https://openalex.org/I4210144804","display_name":"Laboratoire de Recherche en Informatique","ror":"https://ror.org/04e3ktk27","country_code":"FR","type":"facility","lineage":["https://openalex.org/I102197404","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I4210144804","https://openalex.org/I4210159245"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Laura Grigori","raw_affiliation_strings":["Laboratoire de Recherche en Informatique"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire de Recherche en Informatique","institution_ids":["https://openalex.org/I4210144804"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076825233","display_name":"James Demmel","orcid":"https://orcid.org/0000-0003-1145-3745"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"James W. Demmel","raw_affiliation_strings":["Department of Mathematics [Berkeley]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics [Berkeley]","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043042295","display_name":"Hua Xiang","orcid":"https://orcid.org/0000-0002-5094-2376"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hua Xiang","raw_affiliation_strings":["Department of Mathematics [Wuhan]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics [Wuhan]","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.8273,"has_fulltext":false,"cited_by_count":75,"citation_normalized_percentile":{"value":0.97975249,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"32","issue":"4","first_page":"1317","last_page":"1350"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory 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/T10792","display_name":"Matrix Theory 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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9987999796867371,"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"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/gaussian-elimination","display_name":"Gaussian elimination","score":0.7369835376739502},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.6331869959831238},{"id":"https://openalex.org/keywords/schur-complement","display_name":"Schur complement","score":0.6158236265182495},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5514465570449829},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5339585542678833},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5307778120040894},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.506562352180481},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4641360640525818},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.46221229434013367},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3769776523113251},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3746052384376526},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.3499613404273987}],"concepts":[{"id":"https://openalex.org/C126312332","wikidata":"https://www.wikidata.org/wiki/Q2658","display_name":"Gaussian elimination","level":3,"score":0.7369835376739502},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.6331869959831238},{"id":"https://openalex.org/C2731191","wikidata":"https://www.wikidata.org/wiki/Q1778169","display_name":"Schur complement","level":3,"score":0.6158236265182495},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5514465570449829},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5339585542678833},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5307778120040894},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.506562352180481},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4641360640525818},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.46221229434013367},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3769776523113251},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3746052384376526},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.3499613404273987},{"id":"https://openalex.org/C188082640","wikidata":"https://www.wikidata.org/wiki/Q1780899","display_name":"Complementation","level":4,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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/C127716648","wikidata":"https://www.wikidata.org/wiki/Q104053","display_name":"Phenotype","level":3,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/100788926","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100788926","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-00651137v1","is_oa":false,"landing_page_url":"https://inria.hal.science/hal-00651137","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications, 2011, 32, pp.1317-1350. &#x27E8;10.1137/100788926&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W840690709","https://openalex.org/W1480928214","https://openalex.org/W1760551737","https://openalex.org/W1972501001","https://openalex.org/W2007768252","https://openalex.org/W2010747199","https://openalex.org/W2018338919","https://openalex.org/W2020804487","https://openalex.org/W2026237859","https://openalex.org/W2030167104","https://openalex.org/W2053489736","https://openalex.org/W2081114193","https://openalex.org/W2084727637","https://openalex.org/W2098805793","https://openalex.org/W2102248047","https://openalex.org/W2104373803","https://openalex.org/W2115780241","https://openalex.org/W2124480634","https://openalex.org/W2143358426","https://openalex.org/W2157237396","https://openalex.org/W2162322364","https://openalex.org/W2165917639","https://openalex.org/W2169631286","https://openalex.org/W3100417409"],"related_works":["https://openalex.org/W2146459776","https://openalex.org/W2271643833","https://openalex.org/W2471027283","https://openalex.org/W2804034492","https://openalex.org/W2040165403","https://openalex.org/W1796128968","https://openalex.org/W2766762530","https://openalex.org/W68723791","https://openalex.org/W1966532830","https://openalex.org/W1964205397"],"abstract_inverted_index":{"Since":[0],"the":[1,9,46,54,127,142,145,159,162,173,237],"cost":[2,10],"of":[3,11,95,134,164,191,223,240,246],"communication":[4,65,116],"(moving":[5],"data)":[6],"greatly":[7],"exceeds":[8],"doing":[12],"arithmetic":[13],"on":[14,71,113,137,152,181,217,236],"current":[15],"and":[16,39,97,107,169,193,204,220,263],"future":[17],"computing":[18],"platforms,":[19],"we":[20,77,196],"are":[21,158,250],"motivated":[22],"to":[23,79,85,179],"devise":[24],"algorithms":[25],"that":[26,76,89,126,198,227,245],"communicate":[27],"as":[28,30,40,42,80,119,144,161,202],"little":[29],"possible,":[31],"even":[32],"if":[33],"they":[34,43],"do":[35],"slightly":[36,167],"more":[37],"arithmetic,":[38],"long":[41],"still":[44],"get":[45],"right":[47,55],"answer.":[48],"This":[49],"paper":[50],"is":[51,88,117,141,177,229,242],"about":[52],"getting":[53],"answer":[56],"for":[57,253],"such":[58],"an":[59,92],"algorithm.":[60],"It":[61],"discusses":[62],"CALU,":[63,262],"a":[64,72,138,153,182,221],"avoiding":[66],"LU":[67],"factorization":[68],"algorithm":[69],"based":[70],"new":[73],"pivoting":[74,105],"strategy,":[75],"refer":[78],"tournament":[81],"pivoting.":[82],"The":[83,233],"reason":[84],"consider":[86],"CALU":[87,136,175,199,228,241],"it":[90,205],"does":[91],"optimal":[93],"amount":[94],"communication,":[96],"asymptotically":[98],"less":[99],"than":[100,244],"Gaussian":[101],"elimination":[102],"with":[103],"partial":[104],"(GEPP),":[106],"so":[108],"will":[109,200,206],"be":[110,208],"much":[111],"faster":[112],"platforms":[114],"where":[115],"expensive,":[118],"shown":[120],"in":[121,211,231],"previous":[122],"work.":[123],"We":[124],"show":[125,226],"Schur":[128,146],"complement":[129,147],"obtained":[130,148],"after":[131,149],"each":[132],"step":[133],"performing":[135,150],"matrix":[139,155],"A":[140,165,192],"same":[143,160],"GEPP":[151,180,203,255],"larger":[154],"whose":[156],"entries":[157,163,190],"(sometimes":[166],"perturbed)":[168],"zeros.":[170,194],"More":[171],"generally,":[172],"entire":[174],"process":[176],"equivalent":[178],"large,":[183],"but":[184,260],"very":[185,209],"sparse":[186],"matrix,":[187],"formed":[188],"by":[189],"Hence":[195],"expect":[197],"behave":[201],"also":[207],"stable":[210,230],"practice.":[212,232],"In":[213],"addition,":[214],"extensive":[215],"experiments":[216],"random":[218],"matrices":[219,225,252],"set":[222],"special":[224],"upper":[234],"bound":[235],"growth":[238,258],"factor":[239],"worse":[243],"GEPP.":[247],"However,":[248],"there":[249],"Wilkinson-like":[251],"which":[254],"has":[256],"exponential":[257],"factor,":[259],"not":[261],"vice-versa.":[264]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":11},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":10},{"year":2012,"cited_by_count":4}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
