{"id":"https://openalex.org/W2082222857","doi":"https://doi.org/10.1145/1024074.1024080","title":"Algorithm 836","display_name":"Algorithm 836","publication_year":2004,"publication_date":"2004-09-01","ids":{"openalex":"https://openalex.org/W2082222857","doi":"https://doi.org/10.1145/1024074.1024080","mag":"2082222857"},"language":"en","primary_location":{"id":"doi:10.1145/1024074.1024080","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1024074.1024080","pdf_url":null,"source":{"id":"https://openalex.org/S163326656","display_name":"ACM Transactions on Mathematical Software","issn_l":"0098-3500","issn":["0098-3500","1557-7295"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Mathematical Software","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/A5069178025","display_name":"Timothy A. Davis","orcid":"https://orcid.org/0000-0001-7614-6899"},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Timothy A. Davis","raw_affiliation_strings":["University of Florida, Gainesville, FL"],"affiliations":[{"raw_affiliation_string":"University of Florida, Gainesville, FL","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108223550","display_name":"John R. Gilbert","orcid":null},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"John R. Gilbert","raw_affiliation_strings":["University of California, Santa Barbara, CA","University of California, Santa Barbara, Ca#TAB#"],"affiliations":[{"raw_affiliation_string":"University of California, Santa Barbara, CA","institution_ids":["https://openalex.org/I154570441"]},{"raw_affiliation_string":"University of California, Santa Barbara, Ca#TAB#","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013958279","display_name":"Stefan I. Larimore","orcid":null},"institutions":[{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Stefan I. Larimore","raw_affiliation_strings":["Microsoft, Inc., Redmond, WA","Microsoft Inc, Redmond, WA#TAB#"],"affiliations":[{"raw_affiliation_string":"Microsoft, Inc., Redmond, WA","institution_ids":["https://openalex.org/I1290206253"]},{"raw_affiliation_string":"Microsoft Inc, Redmond, WA#TAB#","institution_ids":["https://openalex.org/I1290206253"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056131016","display_name":"Esmond Ng","orcid":"https://orcid.org/0000-0002-4535-6348"},"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":"Esmond G. Ng","raw_affiliation_strings":["Lawrence Berkeley National Laboratory, Berkeley, CA"],"affiliations":[{"raw_affiliation_string":"Lawrence Berkeley National Laboratory, Berkeley, CA","institution_ids":["https://openalex.org/I148283060"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5069178025"],"corresponding_institution_ids":["https://openalex.org/I33213144"],"apc_list":null,"apc_paid":null,"fwci":3.1424,"has_fulltext":false,"cited_by_count":114,"citation_normalized_percentile":{"value":0.91560423,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"30","issue":"3","first_page":"377","last_page":"380"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9994999766349792,"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"}},{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.994700014591217,"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/cholesky-decomposition","display_name":"Cholesky decomposition","score":0.7509785294532776},{"id":"https://openalex.org/keywords/incomplete-cholesky-factorization","display_name":"Incomplete Cholesky factorization","score":0.6303260922431946},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.6218733191490173},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.5763338208198547},{"id":"https://openalex.org/keywords/incomplete-lu-factorization","display_name":"Incomplete LU factorization","score":0.5653521418571472},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.5485287308692932},{"id":"https://openalex.org/keywords/qr-decomposition","display_name":"QR decomposition","score":0.5445958375930786},{"id":"https://openalex.org/keywords/matlab","display_name":"MATLAB","score":0.48859554529190063},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4864032566547394},{"id":"https://openalex.org/keywords/row","display_name":"Row","score":0.478497177362442},{"id":"https://openalex.org/keywords/minimum-degree-algorithm","display_name":"Minimum degree algorithm","score":0.4358377456665039},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42465919256210327},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4059753119945526},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.3680269718170166},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.36793142557144165},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.08712303638458252}],"concepts":[{"id":"https://openalex.org/C34727166","wikidata":"https://www.wikidata.org/wiki/Q515375","display_name":"Cholesky decomposition","level":3,"score":0.7509785294532776},{"id":"https://openalex.org/C44363057","wikidata":"https://www.wikidata.org/wiki/Q6015160","display_name":"Incomplete Cholesky factorization","level":4,"score":0.6303260922431946},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.6218733191490173},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.5763338208198547},{"id":"https://openalex.org/C134978465","wikidata":"https://www.wikidata.org/wiki/Q1654069","display_name":"Incomplete LU factorization","level":4,"score":0.5653521418571472},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.5485287308692932},{"id":"https://openalex.org/C188060507","wikidata":"https://www.wikidata.org/wiki/Q653242","display_name":"QR decomposition","level":3,"score":0.5445958375930786},{"id":"https://openalex.org/C2780365114","wikidata":"https://www.wikidata.org/wiki/Q169478","display_name":"MATLAB","level":2,"score":0.48859554529190063},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4864032566547394},{"id":"https://openalex.org/C135598885","wikidata":"https://www.wikidata.org/wiki/Q1366302","display_name":"Row","level":2,"score":0.478497177362442},{"id":"https://openalex.org/C46085209","wikidata":"https://www.wikidata.org/wiki/Q17098969","display_name":"Minimum degree algorithm","level":5,"score":0.4358377456665039},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42465919256210327},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4059753119945526},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.3680269718170166},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.36793142557144165},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.08712303638458252},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating 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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1024074.1024080","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1024074.1024080","pdf_url":null,"source":{"id":"https://openalex.org/S163326656","display_name":"ACM Transactions on Mathematical Software","issn_l":"0098-3500","issn":["0098-3500","1557-7295"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Mathematical Software","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W2007259720","https://openalex.org/W2014730252","https://openalex.org/W2020561008","https://openalex.org/W2038205735","https://openalex.org/W2167797964","https://openalex.org/W2503454203"],"related_works":["https://openalex.org/W1987177655","https://openalex.org/W2381435995","https://openalex.org/W2063952346","https://openalex.org/W1991619898","https://openalex.org/W2739115385","https://openalex.org/W2397810771","https://openalex.org/W2041700769","https://openalex.org/W54819768","https://openalex.org/W2074550915","https://openalex.org/W2127287720"],"abstract_inverted_index":{"Two":[0],"codes":[1],"are":[2,57,109],"discussed,":[3],"COLAMD":[4,60,67],"and":[5,34,48,61,75,86,98,114],"SYMAMD,":[6,62],"that":[7,93],"compute":[8],"approximate":[9],"minimum":[10],"degree":[11],"orderings":[12,56],"for":[13,71,102],"sparse":[14,20,36,72],"matrices":[15,79],"in":[16,95,112,122],"two":[17,107],"contexts:":[18],"(1)":[19],"partial":[21],"pivoting,":[22],"which":[23,39],"requires":[24,40],"a":[25,41],"sparsity":[26],"preserving":[27],"column":[28],"pre-ordering":[29],"prior":[30],"to":[31],"numerical":[32],"factorization,":[33,38,74],"(2)":[35],"Cholesky":[37],"symmetric":[42],"permutation":[43],"of":[44,50,78,80],"both":[45,111],"the":[46,51,76,81],"rows":[47],"columns":[49],"matrix":[52],"being":[53],"factorized.":[54],"These":[55],"computed":[58],"by":[59],"respectively.":[63],"The":[64,106],"ordering":[65],"from":[66],"is":[68],"also":[69],"suitable":[70],"QR":[73],"factorization":[77],"form":[82],"A":[83,85],"T":[84,88],"AA":[87],",":[89],"such":[90],"as":[91,119],"those":[92],"arise":[94],"least-squares":[96],"problems":[97],"interior":[99],"point":[100],"methods":[101],"linear":[103],"programming":[104],"problems.":[105],"routines":[108,121],"available":[110],"MATLAB":[113,123],"C-callable":[115],"forms.":[116],"They":[117],"appear":[118],"built-in":[120],"Version":[124],"6.0.":[125]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":11},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":12},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":11}],"updated_date":"2026-03-28T08:17:26.163206","created_date":"2016-06-24T00:00:00"}
