{"id":"https://openalex.org/W2033130314","doi":"https://doi.org/10.1137/120863691","title":"LU Factorization with Panel Rank Revealing Pivoting and Its Communication Avoiding Version","display_name":"LU Factorization with Panel Rank Revealing Pivoting and Its Communication Avoiding Version","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2033130314","doi":"https://doi.org/10.1137/120863691","mag":"2033130314"},"language":"en","primary_location":{"id":"doi:10.1137/120863691","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120863691","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":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1208.2451","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013949089","display_name":"Amal Khabou","orcid":null},"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":true,"raw_author_name":"Amal Khabou","raw_affiliation_strings":["Laboratoire de recherche en informatique"],"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]"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics [Berkeley]","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040521001","display_name":"Laura Grigori","orcid":"https://orcid.org/0000-0002-5880-1076"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Laura Grigori","raw_affiliation_strings":["Algorithms and parallel tools for integrated numerical simulations"],"affiliations":[{"raw_affiliation_string":"Algorithms and parallel tools for integrated numerical simulations","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103226688","display_name":"Ming Gu","orcid":"https://orcid.org/0009-0005-2951-5256"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ming Gu","raw_affiliation_strings":["Department of Mathematics [Berkeley]"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics [Berkeley]","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5013949089"],"corresponding_institution_ids":["https://openalex.org/I4210144804"],"apc_list":null,"apc_paid":null,"fwci":5.9176,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.96443938,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"34","issue":"3","first_page":"1401","last_page":"1429"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.996999979019165,"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":0.996999979019165,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9937000274658203,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10575","display_name":"Wireless Communication Networks Research","score":0.991100013256073,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/qr-decomposition","display_name":"QR decomposition","score":0.7922476530075073},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.7551612257957458},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.6335659027099609},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5860148668289185},{"id":"https://openalex.org/keywords/gaussian-elimination","display_name":"Gaussian elimination","score":0.5775500535964966},{"id":"https://openalex.org/keywords/lu-decomposition","display_name":"LU decomposition","score":0.5248594284057617},{"id":"https://openalex.org/keywords/selection","display_name":"Selection (genetic algorithm)","score":0.4434587359428406},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4366624057292938},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4268975853919983},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.413222074508667},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.40327513217926025},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3790268301963806},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3497309684753418},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.27724403142929077},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09532129764556885}],"concepts":[{"id":"https://openalex.org/C188060507","wikidata":"https://www.wikidata.org/wiki/Q653242","display_name":"QR decomposition","level":3,"score":0.7922476530075073},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.7551612257957458},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.6335659027099609},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5860148668289185},{"id":"https://openalex.org/C126312332","wikidata":"https://www.wikidata.org/wiki/Q2658","display_name":"Gaussian elimination","level":3,"score":0.5775500535964966},{"id":"https://openalex.org/C123213974","wikidata":"https://www.wikidata.org/wiki/Q833089","display_name":"LU decomposition","level":4,"score":0.5248594284057617},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.4434587359428406},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4366624057292938},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4268975853919983},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.413222074508667},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.40327513217926025},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3790268301963806},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3497309684753418},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.27724403142929077},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09532129764556885},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":11,"locations":[{"id":"doi:10.1137/120863691","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120863691","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:eprints.maths.manchester.ac.uk.MIMS.EPrints:1958","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400452","display_name":"MIMS EPrints (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"MIMS Preprint"},{"id":"pmh:oai:arXiv.org:1208.2451","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1208.2451","pdf_url":"https://arxiv.org/pdf/1208.2451","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":"","raw_type":"text"},{"id":"pmh:oai:berkeley.edu:28722-bk0010r6s3r","is_oa":false,"landing_page_url":"http://techreports.lib.berkeley.edu/accessPages/EECS-2012-15.html","pdf_url":null,"source":{"id":"https://openalex.org/S7407050879","display_name":"UC Berkeley","issn_l":null,"issn":[],"is_oa":false,"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":"","raw_type":"technical reports"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.220.4890","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.220.4890","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hal.inria.fr/docs/00/66/28/36/PDF/RR-7867.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.221.2471","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.221.2471","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.eecs.berkeley.edu/Pubs/TechRpts/2012/EECS-2012-15.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.232.7079","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.232.7079","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.netlib.org/lapack/lawnspdf/lawn263.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.708.5579","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.708.5579","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://who.rocq.inria.fr/Laura.Grigori/Papers/caluprrp.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00723564v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-00723564","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"[Research Report] RR-7867, INRIA. 2012","raw_type":"Reports"},{"id":"pmh:oai:HAL:hal-00872145v1","is_oa":false,"landing_page_url":"https://inria.hal.science/hal-00872145","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":"http://epubs.siam.org/toc/sjmael/34/3","raw_type":"Journal articles"},{"id":"doi:10.48550/arxiv.1208.2451","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1208.2451","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1208.2451","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1208.2451","pdf_url":"https://arxiv.org/pdf/1208.2451","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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1669598709","https://openalex.org/W1760551737","https://openalex.org/W1972501001","https://openalex.org/W1976662650","https://openalex.org/W1999202513","https://openalex.org/W2000692285","https://openalex.org/W2008170215","https://openalex.org/W2010747199","https://openalex.org/W2018338919","https://openalex.org/W2023689870","https://openalex.org/W2030167104","https://openalex.org/W2041364558","https://openalex.org/W2053489736","https://openalex.org/W2084727637","https://openalex.org/W2097733694","https://openalex.org/W2102248047","https://openalex.org/W2104373803","https://openalex.org/W2104760562","https://openalex.org/W2115780241","https://openalex.org/W2119233169","https://openalex.org/W2143358426","https://openalex.org/W2157237396","https://openalex.org/W2163688235","https://openalex.org/W2165917639","https://openalex.org/W2169631286","https://openalex.org/W3022909171","https://openalex.org/W3100417409"],"related_works":["https://openalex.org/W5176254","https://openalex.org/W1966287322","https://openalex.org/W2561626198","https://openalex.org/W4244491923","https://openalex.org/W2078349096","https://openalex.org/W2766762530","https://openalex.org/W4388311419","https://openalex.org/W4240431572","https://openalex.org/W1973739845","https://openalex.org/W2015045768"],"abstract_inverted_index":{"We":[0,94,180],"present":[1,182],"block":[2,60,166,183,188],"LU":[3],"factorization":[4,147,168],"with":[5,31,35,199,232],"panel":[6,21,56,112],"rank":[7,18,69,215],"revealing":[8,19,70,216],"pivoting":[9,33],"(block":[10],"LU_PRRP),":[11],"a":[12,36,64,90,185,233],"decomposition":[13],"algorithm":[14],"based":[15,195],"on":[16,196,284],"strong":[17,68,214],"QR":[20,71,217],"factorization.":[22,218],"Block":[23,219,270],"LU_PRRP":[24,167,189],"is":[25,51,63,74,89,113,129,149,159,194,221,248,268,272,279],"more":[26,160,222,274],"stable":[27,152,223,275],"than":[28,224],"Gaussian":[29],"elimination":[30],"partial":[32],"(GEPP),":[34],"theoretical":[37,234],"upper":[38,131,235,260],"bound":[39,132,236,261],"of":[40,44,54,66,77,79,92,110,133,137,187,202,208,230,237,241,251,262,266],"the":[41,52,55,59,67,75,80,98,108,111,130,134,145,200,203,209,226,238,249,252,263],"growth":[42,135,239,264],"factor":[43,136,240,265],"$(1+":[45,242],"\\tau":[46,243],"b)^{(n/":[47],"b)-1}$,":[48],"where":[49,127,246],"$b$":[50],"size":[53,109],"used":[57,255],"during":[58,256],"factorization,":[61,72],"$\\tau$":[62],"parameter":[65],"$n$":[73],"number":[76],"columns":[78],"matrix,":[81],"and":[82,117,193,278,287],"for":[83],"simplicity":[84],"we":[85],"assume":[86,96],"that":[87,100,144,190],"n":[88],"multiple":[91],"b.":[93],"also":[95,181,273],"throughout":[97],"paper":[99],"$2\\leq":[101],"b":[102],"\\ll":[103,125],"n$.":[104],"For":[105],"example,":[106],"if":[107],"$b":[114],"=":[115,119,123],"64$,":[116],"$\\tau":[118],"2$,":[120],"then":[121],"$(1+2b)^{(n/b)-1}":[122],"(1.079)^{n-64}":[124],"2^{n-1}$,":[126],"$2^{n-1}$":[128],"GEPP.":[138,179],"Our":[139],"extensive":[140],"numerical":[141],"experiments":[142],"show":[143],"new":[146],"scheme":[148],"as":[150,153],"numerically":[151],"GEPP":[154,286],"in":[155,276],"practice,":[156],"but":[157],"it":[158],"resistant":[161,280],"to":[162,178,281],"pathological":[163,282],"cases.":[164],"The":[165,259],"does":[169],"only":[170],"$O(n^2":[171],"b)$":[172],"additional":[173],"floating":[174],"point":[175],"operations":[176],"compared":[177],"CALU_PRRP,":[184],"version":[186,229],"minimizes":[191],"communication":[192,227],"tournament":[197,210,257],"pivoting,":[198],"selection":[201],"pivots":[204],"at":[205],"each":[206],"step":[207],"being":[211],"performed":[212],"via":[213],"CALU_PRRP":[220,271],"CALU,":[225],"avoiding":[228],"GEPP,":[231],"b)^{{n\\over":[244],"b}(H+1)-1}$,":[245],"$H$":[247],"height":[250],"reduction":[253],"tree":[254],"pivoting.":[258],"CALU":[267,288],"$2^{n(H+1)-1}$.":[269],"practice":[277],"cases":[283],"which":[285],"fail.":[289]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":5}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2019-06-27T00:00:00"}