{"id":"https://openalex.org/W1987322414","doi":"https://doi.org/10.1137/050629343","title":"Symbolic and Exact Structure Prediction for Sparse Gaussian Elimination with Partial Pivoting","display_name":"Symbolic and Exact Structure Prediction for Sparse Gaussian Elimination with Partial Pivoting","publication_year":2008,"publication_date":"2008-12-22","ids":{"openalex":"https://openalex.org/W1987322414","doi":"https://doi.org/10.1137/050629343","mag":"1987322414"},"language":"en","primary_location":{"id":"doi:10.1137/050629343","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050629343","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":[],"countries":[],"is_corresponding":false,"raw_author_name":"Laura Grigori","raw_affiliation_strings":["Laura.Grigori@inria.fr#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laura.Grigori@inria.fr#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108223550","display_name":"John R. Gilbert","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"John R. Gilbert","raw_affiliation_strings":["gilbert@cs.ucsb.edu#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"gilbert@cs.ucsb.edu#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110214133","display_name":"Michel Cosnard","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michel Cosnard","raw_affiliation_strings":["Michel.Cosnard@inria.fr#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Michel.Cosnard@inria.fr#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.06928624,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"30","issue":"4","first_page":"1520","last_page":"1545"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9994999766349792,"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":0.9994999766349792,"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/T12303","display_name":"Tensor decomposition and applications","score":0.9937999844551086,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9921000003814697,"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":0.7848954200744629},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7548209428787231},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.6430471539497375},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.6181230545043945},{"id":"https://openalex.org/keywords/merge","display_name":"Merge (version control)","score":0.5809198021888733},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5318491458892822},{"id":"https://openalex.org/keywords/block-matrix","display_name":"Block matrix","score":0.47793012857437134},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4354206323623657},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.344917356967926},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.257843017578125},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1276019811630249}],"concepts":[{"id":"https://openalex.org/C126312332","wikidata":"https://www.wikidata.org/wiki/Q2658","display_name":"Gaussian elimination","level":3,"score":0.7848954200744629},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7548209428787231},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.6430471539497375},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.6181230545043945},{"id":"https://openalex.org/C197129107","wikidata":"https://www.wikidata.org/wiki/Q1921621","display_name":"Merge (version control)","level":2,"score":0.5809198021888733},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5318491458892822},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.47793012857437134},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4354206323623657},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.344917356967926},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.257843017578125},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1276019811630249},{"id":"https://openalex.org/C23123220","wikidata":"https://www.wikidata.org/wiki/Q816826","display_name":"Information retrieval","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/050629343","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050629343","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1568175246","https://openalex.org/W1704590117","https://openalex.org/W1972859808","https://openalex.org/W1981404639","https://openalex.org/W2018664150","https://openalex.org/W2021108117","https://openalex.org/W2028495395","https://openalex.org/W2038205735","https://openalex.org/W2055094346","https://openalex.org/W2055791798","https://openalex.org/W2062090047","https://openalex.org/W2064762577","https://openalex.org/W2069792133","https://openalex.org/W2089341221","https://openalex.org/W2091978199","https://openalex.org/W2093992309","https://openalex.org/W2128978199","https://openalex.org/W2141025928","https://openalex.org/W2141331848","https://openalex.org/W2143474538","https://openalex.org/W2798909945"],"related_works":["https://openalex.org/W2271643833","https://openalex.org/W1969557273","https://openalex.org/W2064955113","https://openalex.org/W2023689870","https://openalex.org/W2913918688","https://openalex.org/W2170271555","https://openalex.org/W2952318043","https://openalex.org/W2001342884","https://openalex.org/W1991995462","https://openalex.org/W2766762530"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3,21,89],"consider":[4,22,90],"two":[5],"structure":[6,29,46,99,117,166,179],"prediction":[7,43],"problems":[8],"of":[9,17,25,30,44,63,79,84,93,100,118,122,156,180],"interest":[10],"in":[11,151],"Gaussian":[12,54,123],"elimination":[13,124],"with":[14,125],"partial":[15,126],"pivoting":[16,127],"sparse":[18],"matrices.":[19],"First,":[20],"the":[23,27,31,37,45,64,77,91,98,106,115,132,135,143,148,168,177,190,198,211],"problem":[24,92],"determining":[26],"nonzero":[28,116,149,178],"factors":[32],"L":[33,101,119,181],"and":[34,82,102,120,146,182],"U":[35,103,121,183],"during":[36,53],"factorization.":[38,108],"We":[39,109,194],"present":[40,110],"an":[41],"exact":[42,112],"that":[47,68,72,134,147,164,197],"identifies":[48],"some":[49],"numeric":[50,57],"cancellations":[51,58],"appearing":[52],"elimination.":[55],"The":[56],"are":[59,69,153],"related":[60],"to":[61,76,105],"submatrices":[62],"input":[65],"matrix":[66,136],"A":[67,137,152],"structurally":[70],"singular,":[71],"is,":[73],"singular":[74],"due":[75],"arrangements":[78],"their":[80,85],"nonzeros,":[81],"independent":[83,155],"numerical":[86,107],"values.":[87],"Second,":[88],"estimating":[94],"upper":[95],"bounds":[96,113],"for":[97,114,176,207],"prior":[104],"tight":[111,174,204],"$PA":[128],"=":[129],"LU$":[130],"under":[131,184],"assumption":[133],"satisfies":[138],"a":[139,165,173,185,203],"combinatorial":[140,187],"property,":[141,145],"namely,":[142,189],"Hall":[144,192,212],"values":[150],"algebraically":[154],"each":[157],"other.":[158],"This":[159],"complements":[160],"existing":[161],"work":[162],"showing":[163],"called":[167],"row":[169,199],"merge":[170,200],"graph":[171,201],"represents":[172,202],"bound":[175,206],"stronger":[186],"assumption,":[188],"strong":[191],"property.":[193,213],"also":[195],"show":[196],"symbolic":[205],"matrices":[208],"satisfying":[209],"only":[210]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}