{"id":"https://openalex.org/W1521924480","doi":"https://doi.org/10.1137/s0895479801385037","title":"Nested-Dissection Orderings for Sparse LU with Partial Pivoting","display_name":"Nested-Dissection Orderings for Sparse LU with Partial Pivoting","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W1521924480","doi":"https://doi.org/10.1137/s0895479801385037","mag":"1521924480"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479801385037","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479801385037","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/A5086340059","display_name":"Igor Brainman","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Igor Brainman","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5056808449","display_name":"Sivan Toledo","orcid":"https://orcid.org/0000-0002-9524-7115"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sivan Toledo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.05483564,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"23","issue":"4","first_page":"998","last_page":"1012"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","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"}},"topics":[{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","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"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9908999800682068,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9883000254631042,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cholesky-decomposition","display_name":"Cholesky decomposition","score":0.7509617805480957},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.6811545491218567},{"id":"https://openalex.org/keywords/heuristics","display_name":"Heuristics","score":0.6218571662902832},{"id":"https://openalex.org/keywords/column","display_name":"Column (typography)","score":0.5981753468513489},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.5818939208984375},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5124664902687073},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.4958735406398773},{"id":"https://openalex.org/keywords/lu-decomposition","display_name":"LU decomposition","score":0.47500526905059814},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4746323823928833},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47128668427467346},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4652126133441925},{"id":"https://openalex.org/keywords/gaussian-elimination","display_name":"Gaussian elimination","score":0.44813498854637146},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.44296544790267944},{"id":"https://openalex.org/keywords/sparse-approximation","display_name":"Sparse approximation","score":0.4373745322227478},{"id":"https://openalex.org/keywords/incomplete-cholesky-factorization","display_name":"Incomplete Cholesky factorization","score":0.4119487702846527},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3894880414009094},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.36536911129951477},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2871091663837433}],"concepts":[{"id":"https://openalex.org/C34727166","wikidata":"https://www.wikidata.org/wiki/Q515375","display_name":"Cholesky decomposition","level":3,"score":0.7509617805480957},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.6811545491218567},{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.6218571662902832},{"id":"https://openalex.org/C2780551164","wikidata":"https://www.wikidata.org/wiki/Q2306599","display_name":"Column (typography)","level":3,"score":0.5981753468513489},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.5818939208984375},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5124664902687073},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.4958735406398773},{"id":"https://openalex.org/C123213974","wikidata":"https://www.wikidata.org/wiki/Q833089","display_name":"LU decomposition","level":4,"score":0.47500526905059814},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4746323823928833},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47128668427467346},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4652126133441925},{"id":"https://openalex.org/C126312332","wikidata":"https://www.wikidata.org/wiki/Q2658","display_name":"Gaussian elimination","level":3,"score":0.44813498854637146},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.44296544790267944},{"id":"https://openalex.org/C124066611","wikidata":"https://www.wikidata.org/wiki/Q28684319","display_name":"Sparse approximation","level":2,"score":0.4373745322227478},{"id":"https://openalex.org/C44363057","wikidata":"https://www.wikidata.org/wiki/Q6015160","display_name":"Incomplete Cholesky factorization","level":4,"score":0.4119487702846527},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3894880414009094},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.36536911129951477},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2871091663837433},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","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/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/s0895479801385037","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479801385037","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:CiteSeerX.psu:10.1.1.29.182","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.29.182","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.tau.ac.il/~sivan/Pubs/wide.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.32.6246","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.32.6246","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.tau.ac.il/~stoledo/Pubs/naa00-wide.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.381.1751","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.381.1751","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.tau.ac.il/~stoledo/Bib/Pubs/wide-simax.pdf","raw_type":"text"},{"id":"mag:1521924480","is_oa":false,"landing_page_url":"https://dblp.uni-trier.de/db/conf/ppsc/ppsc2001.html#BrainmanT01","pdf_url":null,"source":{"id":"https://openalex.org/S4306522931","display_name":"PPSC","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"PPSC","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W2026930830","https://openalex.org/W2038205735","https://openalex.org/W2054816610","https://openalex.org/W2068543948","https://openalex.org/W2088160222","https://openalex.org/W2093992309","https://openalex.org/W2096559782","https://openalex.org/W2137541800"],"related_works":["https://openalex.org/W1993166013","https://openalex.org/W1779326604","https://openalex.org/W1603047746","https://openalex.org/W2038205735","https://openalex.org/W91483751","https://openalex.org/W2015874996","https://openalex.org/W156354643","https://openalex.org/W2097085687","https://openalex.org/W67540999","https://openalex.org/W2745693163","https://openalex.org/W253708524","https://openalex.org/W3098043076","https://openalex.org/W2183234330","https://openalex.org/W2053999255","https://openalex.org/W2025389417","https://openalex.org/W107449615","https://openalex.org/W2015628020","https://openalex.org/W2084848530","https://openalex.org/W3130355893","https://openalex.org/W1832282200"],"abstract_inverted_index":{"We":[0,132],"describe":[1],"the":[2,50,53,61,65,72,86,89,145,158,165,180],"implementation":[3],"and":[4,25,32,149],"performance":[5],"of":[6,52,92,114,125,138,175,177,187],"a":[7,80,111,123,136,185],"novel":[8],"fill-minimization":[9],"ordering":[10,38,113],"technique":[11,20],"for":[12,37,41],"sparse":[13,39],"LU":[14,42,166],"factorization":[15],"with":[16,43,135],"partial":[17,44],"pivoting.":[18],"The":[19,162],"was":[21],"proposed":[22],"by":[23,60,182],"Gilbert":[24],"Schreiber":[26],"in":[27,88,179],"1980":[28],"but":[29],"never":[30,121],"implemented":[31],"tested.":[33],"Like":[34],"other":[35,70],"techniques":[36],"matrices":[40,173],"pivoting,":[45],"our":[46,105],"new":[47,106],"method":[48,107,146,163],"preorders":[49],"columns":[51],"matrix":[54],"(the":[55],"row":[56],"permutation":[57,74,81],"is":[58,79,108,147],"chosen":[59],"pivoting":[62],"sequence":[63],"during":[64],"numerical":[66],"factorization).":[67],"Also":[68],"like":[69],"methods,":[71],"column":[73],"Q":[75],"that":[76,82,144,150],"we":[77],"select":[78],"attempts":[83],"to":[84,157],"reduce":[85,153],"fill":[87,154],"Cholesky":[90],"factor":[91,186],"QT":[93],"ATAQ.":[94],"Unlike":[95],"existing":[96,160],"column-ordering":[97],"techniques,":[98],"which":[99,128],"all":[100],"rely":[101],"on":[102,110,169],"minimum-degree":[103],"heuristics,":[104],"based":[109],"nested-dissection":[112],"A":[115,139],"T":[116],"A.":[117],"Our":[118,141],"algorithm,":[119],"however,":[120],"computes":[122],"representation":[124,137],"AT":[126],"A,":[127],"can":[129,152],"be":[130],"expensive.":[131],"only":[133],"work":[134],"itself.":[140],"experiments":[142],"demonstrate":[143],"efficient":[148],"it":[151],"significantly":[155],"relative":[156],"best":[159],"methods.":[161],"reduces":[164],"running":[167],"time":[168],"some":[170],"very":[171],"large":[172],"(tens":[174],"millions":[176],"nonzeros":[178],"factors)":[181],"more":[183],"than":[184],"2.":[188]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}