{"id":"https://openalex.org/W2053266474","doi":"https://doi.org/10.1137/050638102","title":"Parallel Symbolic Factorization for Sparse LU with Static Pivoting","display_name":"Parallel Symbolic Factorization for Sparse LU with Static Pivoting","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2053266474","doi":"https://doi.org/10.1137/050638102","mag":"2053266474"},"language":"en","primary_location":{"id":"doi:10.1137/050638102","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050638102","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Laura Grigori","raw_affiliation_strings":["INRIA Futurs, Parc Club Orsay Universite, 4 rue Jacques Monod, Bat G, 91893 Orsay, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"INRIA Futurs, Parc Club Orsay Universite, 4 rue Jacques Monod, Bat G, 91893 Orsay, France","institution_ids":["https://openalex.org/I1326498283"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076825233","display_name":"James Demmel","orcid":"https://orcid.org/0000-0003-1145-3745"},"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":false,"raw_author_name":"James W. Demmel","raw_affiliation_strings":["Computer Science Division and Mathematics Department, University of California at Berkeley, Berkeley, CA 94720-1776"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science Division and Mathematics Department, University of California at Berkeley, Berkeley, CA 94720-1776","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006873445","display_name":"Xiaoye Sherry Li","orcid":"https://orcid.org/0000-0002-0747-698X"},"institutions":[{"id":"https://openalex.org/I148283060","display_name":"Lawrence Berkeley National Laboratory","ror":"https://ror.org/02jbv0t02","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I148283060","https://openalex.org/I39565521"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xiaoye S. Li","raw_affiliation_strings":["Lawrence Berkeley National Laboratory, One Cyclotron Road, Mail Stop 50F-1650, Berkeley, CA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lawrence Berkeley National Laboratory, One Cyclotron Road, Mail Stop 50F-1650, Berkeley, CA","institution_ids":["https://openalex.org/I148283060"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.7437,"has_fulltext":false,"cited_by_count":56,"citation_normalized_percentile":{"value":0.93007863,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"29","issue":"3","first_page":"1289","last_page":"1314"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9993000030517578,"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":0.9993000030517578,"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/T10829","display_name":"Interconnection Networks and Systems","score":0.9993000030517578,"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"}},{"id":"https://openalex.org/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9983000159263611,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.6995062232017517},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6492334008216858},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.5579487681388855},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.5454467535018921},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.540399968624115},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.533397912979126},{"id":"https://openalex.org/keywords/tree-traversal","display_name":"Tree traversal","score":0.5262219905853271},{"id":"https://openalex.org/keywords/parallel-algorithm","display_name":"Parallel algorithm","score":0.5080106258392334},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4658812880516052},{"id":"https://openalex.org/keywords/bottleneck","display_name":"Bottleneck","score":0.4441666007041931}],"concepts":[{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.6995062232017517},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6492334008216858},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.5579487681388855},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.5454467535018921},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.540399968624115},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.533397912979126},{"id":"https://openalex.org/C140745168","wikidata":"https://www.wikidata.org/wiki/Q1210082","display_name":"Tree traversal","level":2,"score":0.5262219905853271},{"id":"https://openalex.org/C120373497","wikidata":"https://www.wikidata.org/wiki/Q1087987","display_name":"Parallel algorithm","level":2,"score":0.5080106258392334},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4658812880516052},{"id":"https://openalex.org/C2780513914","wikidata":"https://www.wikidata.org/wiki/Q18210350","display_name":"Bottleneck","level":2,"score":0.4441666007041931},{"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/C149635348","wikidata":"https://www.wikidata.org/wiki/Q193040","display_name":"Embedded system","level":1,"score":0.0},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/050638102","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050638102","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.105.9411","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.105.9411","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www-rocq.inria.fr/who/Laura.Grigori/Papers/psymbFact_SISC.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.709.2609","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.709.2609","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/psymbFact_SISC.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.73.6923","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.73.6923","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://crd.lbl.gov/~xiaoye/pSymbfact.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1348557892","display_name":null,"funder_award_id":"DE-AC03-76SF00098","funder_id":"https://openalex.org/F4320337506","funder_display_name":"Advanced Scientific Computing Research"},{"id":"https://openalex.org/G1520514311","display_name":"TERASCALE OPTIMAL BDE         SIMULATIONS (TOPS) CENTER","funder_award_id":"FC02-01ER25478","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G1643223109","display_name":null,"funder_award_id":"AC03-76SF00098","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G3658891630","display_name":"TOWARDS OPTIMAL PETASCALE SIMULTATIONS (TOPS)","funder_award_id":"FC02-06ER25786","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G4323016164","display_name":null,"funder_award_id":"DE-AC03-76SF00098","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G6586271056","display_name":null,"funder_award_id":"DE-AC03-76SF00098","funder_id":"https://openalex.org/F4320332359","funder_display_name":"Office of Science"},{"id":"https://openalex.org/G7245193638","display_name":null,"funder_award_id":"DE-AC03","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"}],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320332359","display_name":"Office of Science","ror":"https://ror.org/00mmn6b08"},{"id":"https://openalex.org/F4320337506","display_name":"Advanced Scientific Computing Research","ror":"https://ror.org/0012c7r22"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W69764252","https://openalex.org/W1509994495","https://openalex.org/W1966461475","https://openalex.org/W1968235986","https://openalex.org/W1981885118","https://openalex.org/W2016441057","https://openalex.org/W2021108117","https://openalex.org/W2023521505","https://openalex.org/W2038205735","https://openalex.org/W2055791798","https://openalex.org/W2069849438","https://openalex.org/W2084848530","https://openalex.org/W2089341221","https://openalex.org/W2118953734","https://openalex.org/W2127144731","https://openalex.org/W2141331848","https://openalex.org/W2143131337","https://openalex.org/W3202477519"],"related_works":["https://openalex.org/W2136735429","https://openalex.org/W170547082","https://openalex.org/W1657880117","https://openalex.org/W2595172197","https://openalex.org/W71033917","https://openalex.org/W2011231227","https://openalex.org/W77087835","https://openalex.org/W1562918010","https://openalex.org/W2799252526","https://openalex.org/W1549801657"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"the":[3,30,36,63,66,70,75,79,100,112,147,152,156,163,168,175,178,188,192,204],"design":[4],"and":[5,86,108,120,135],"implementation":[6],"of":[7,32,99,106,118,124,155,167,177,203],"a":[8,24,40,57,82,87,96,104,138,198],"memory":[9,153,165,201],"scalable":[10],"parallel":[11,21,52,93,148,169,189,205],"symbolic":[12,157,193],"factorization":[13,158,194],"algorithm":[14,22,94,113,130,149,190],"for":[15,45,51],"general":[16],"sparse":[17],"unsymmetric":[18],"matrices.":[19],"Our":[20],"uses":[23],"graph":[25,31],"partitioning":[26,55],"approach,":[27],"applied":[28],"to":[29,34,73,89],"$|A|+|A|^T$,":[33],"partition":[35],"matrix":[37,77],"in":[38,133],"such":[39],"way":[41],"that":[42,146],"is":[43,131,182],"good":[44],"sparsity":[46],"preservation":[47],"as":[48,50,160,162],"well":[49,161],"factorization.":[53],"The":[54,92,129],"yields":[56],"so-called":[58],"separator":[59,71,101],"tree":[60,72],"which":[61,181],"represents":[62],"dependencies":[64],"among":[65],"computations.":[67],"We":[68],"use":[69],"distribute":[74],"input":[76],"over":[78],"processors":[80],"using":[81],"block":[83],"cyclic":[84],"approach":[85],"subtree":[88],"subprocessor":[90],"mapping.":[91],"performs":[95],"bottom-up":[97],"traversal":[98],"tree.":[102],"With":[103],"combination":[105],"right-looking":[107],"left-looking":[109],"partial":[110],"factorizations,":[111],"obtains":[114],"one":[115,121],"column":[116],"structure":[117,123],"L":[119],"row":[122],"U":[125],"at":[126],"each":[127],"step.":[128],"implemented":[132],"C":[134],"MPI.":[136],"From":[137],"performance":[139],"study":[140],"on":[141],"large":[142],"matrices,":[143],"we":[144],"show":[145],"significantly":[150],"reduces":[151,174],"requirement":[154,166],"step,":[159],"overall":[164],"solver.":[170,206],"It":[171],"also":[172],"often":[173],"runtime":[176],"sequential":[179],"algorithm,":[180],"already":[183],"relatively":[184],"small.":[185],"In":[186],"general,":[187],"prevents":[191],"step":[195],"from":[196],"being":[197],"time":[199],"or":[200],"bottleneck":[202]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":8}],"updated_date":"2026-06-19T17:40:00.097472","created_date":"2025-10-10T00:00:00"}