{"id":"https://openalex.org/W2964248269","doi":"https://doi.org/10.1145/3054948","title":"SYM-ILDL","display_name":"SYM-ILDL","publication_year":2017,"publication_date":"2017-04-11","ids":{"openalex":"https://openalex.org/W2964248269","doi":"https://doi.org/10.1145/3054948","mag":"2964248269"},"language":"en","primary_location":{"id":"doi:10.1145/3054948","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3054948","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/A5070728305","display_name":"Chen Greif","orcid":null},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Chen Greif","raw_affiliation_strings":["University of British Columbia, Vancouver, Canada"],"affiliations":[{"raw_affiliation_string":"University of British Columbia, Vancouver, Canada","institution_ids":["https://openalex.org/I141945490"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012245788","display_name":"Shiwen He","orcid":null},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Shiwen He","raw_affiliation_strings":["University of British Columbia, Vancouver, Canada"],"affiliations":[{"raw_affiliation_string":"University of British Columbia, Vancouver, Canada","institution_ids":["https://openalex.org/I141945490"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101725949","display_name":"Paul Liu","orcid":"https://orcid.org/0000-0002-9386-6609"},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Paul Liu","raw_affiliation_strings":["University of British Columbia, Vancouver, Canada"],"affiliations":[{"raw_affiliation_string":"University of British Columbia, Vancouver, Canada","institution_ids":["https://openalex.org/I141945490"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5070728305"],"corresponding_institution_ids":["https://openalex.org/I141945490"],"apc_list":null,"apc_paid":null,"fwci":1.1356,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.8144943,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"44","issue":"1","first_page":"1","last_page":"21"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"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":0.9998999834060669,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9930999875068665,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9861999750137329,"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/preconditioner","display_name":"Preconditioner","score":0.7932784557342529},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.55887371301651},{"id":"https://openalex.org/keywords/mathematical-software","display_name":"Mathematical software","score":0.5434816479682922},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.499220609664917},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.45315834879875183},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.4452704191207886},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.43953847885131836},{"id":"https://openalex.org/keywords/incomplete-lu-factorization","display_name":"Incomplete LU factorization","score":0.4307388663291931},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.4297259449958801},{"id":"https://openalex.org/keywords/skew","display_name":"Skew","score":0.4242219030857086},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40808209776878357},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.40531909465789795},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.372531533241272},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.35717177391052246},{"id":"https://openalex.org/keywords/computational-science","display_name":"Computational science","score":0.345567524433136},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3443838357925415},{"id":"https://openalex.org/keywords/software","display_name":"Software","score":0.2823324203491211},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.22644099593162537},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.19243529438972473},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08627176284790039},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.06967082619667053}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.7932784557342529},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.55887371301651},{"id":"https://openalex.org/C2778400913","wikidata":"https://www.wikidata.org/wiki/Q1639024","display_name":"Mathematical software","level":3,"score":0.5434816479682922},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.499220609664917},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.45315834879875183},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.4452704191207886},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.43953847885131836},{"id":"https://openalex.org/C134978465","wikidata":"https://www.wikidata.org/wiki/Q1654069","display_name":"Incomplete LU factorization","level":4,"score":0.4307388663291931},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.4297259449958801},{"id":"https://openalex.org/C43711488","wikidata":"https://www.wikidata.org/wiki/Q7534783","display_name":"Skew","level":2,"score":0.4242219030857086},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40808209776878357},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.40531909465789795},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.372531533241272},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.35717177391052246},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.345567524433136},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3443838357925415},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.2823324203491211},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.22644099593162537},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.19243529438972473},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08627176284790039},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.06967082619667053},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3054948","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3054948","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":[{"id":"https://metadata.un.org/sdg/9","display_name":"Industry, innovation and infrastructure","score":0.4099999964237213}],"awards":[],"funders":[{"id":"https://openalex.org/F4320309370","display_name":"University of Pennsylvania","ror":"https://ror.org/00b30xv10"},{"id":"https://openalex.org/F4320323180","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W309938452","https://openalex.org/W1581078542","https://openalex.org/W1585892185","https://openalex.org/W1678750361","https://openalex.org/W1969156340","https://openalex.org/W1969526019","https://openalex.org/W1971440257","https://openalex.org/W1974336758","https://openalex.org/W1974421439","https://openalex.org/W1976437885","https://openalex.org/W1979359234","https://openalex.org/W1981885118","https://openalex.org/W1986310461","https://openalex.org/W1986822694","https://openalex.org/W2014730252","https://openalex.org/W2017226097","https://openalex.org/W2025437891","https://openalex.org/W2031203150","https://openalex.org/W2031392034","https://openalex.org/W2035080386","https://openalex.org/W2052602889","https://openalex.org/W2069488371","https://openalex.org/W2069715122","https://openalex.org/W2069849438","https://openalex.org/W2069857942","https://openalex.org/W2082205234","https://openalex.org/W2087667283","https://openalex.org/W2093365458","https://openalex.org/W2099438994","https://openalex.org/W2103582339","https://openalex.org/W3022909171"],"related_works":["https://openalex.org/W1986651373","https://openalex.org/W2282105799","https://openalex.org/W3160810049","https://openalex.org/W2986665254","https://openalex.org/W2391090443","https://openalex.org/W1994349276","https://openalex.org/W3204470723","https://openalex.org/W2157073722","https://openalex.org/W2107400804","https://openalex.org/W1586500733"],"abstract_inverted_index":{"SYM-ILDL":[0],"is":[1,25,47,67,72,74],"a":[2,26,79,104,108,130],"numerical":[3],"software":[4],"package":[5,66],"that":[6],"computes":[7],"incomplete":[8,30],"LDL":[9],"T":[10],"(ILDL)":[11],"factorizations":[12],"of":[13,22,29,51],"symmetric":[14,38,63,131],"indefinite":[15],"and":[16,35,42,53,71,77,89,98,112,126],"real":[17,57],"skew-symmetric":[18,58],"matrices.":[19],"The":[20,65,84],"core":[21],"the":[23,137],"algorithm":[24],"Crout":[27],"variant":[28],"LU":[31],"(ILU),":[32],"originally":[33],"introduced":[34],"implemented":[36],"for":[37],"matrices":[39,59],"by":[40],"Li":[41],"Saad":[43],"[2005].":[44],"Our":[45],"code":[46,85],"economical":[48],"in":[49,69],"terms":[50],"storage,":[52],"it":[54],"deals":[55],"with":[56,124,129],"as":[60,62,101,103],"well":[61,102],"ones.":[64],"written":[68],"C++":[70],"templated,":[73],"open":[75],"source,":[76],"includes":[78,86],"M":[80],"atlab":[81],"\u2122":[82],"interface.":[83],"built-in":[87,119],"RCM":[88],"AMD":[90],"reordering,":[91],"two":[92,118],"equilibration":[93,111],"strategies,":[94],"threshold":[95],"Bunch-Kaufman":[96],"pivoting,":[97,100],"rook":[99],"wrapper":[105],"to":[106],"MC64,":[107],"popular":[109],"matching-based":[110],"reordering":[113],"algorithm.":[114],"We":[115],"also":[116],"include":[117],"iterative":[120],"solvers:":[121],"SQMR,":[122],"preconditioned":[123,128],"ILDL,":[125],"MINRES,":[127],"positive":[132],"definite":[133],"preconditioner":[134],"based":[135],"on":[136],"ILDL":[138],"factorization.":[139]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2019-07-30T00:00:00"}