{"id":"https://openalex.org/W1990081458","doi":"https://doi.org/10.1002/1099-1506(200010/12)7:7/8<543::aid-nla212>3.0.co;2-v","title":"An incompleteLU-factorization algorithm based on block bordering","display_name":"An incompleteLU-factorization algorithm based on block bordering","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W1990081458","doi":"https://doi.org/10.1002/1099-1506(200010/12)7:7/8<543::aid-nla212>3.0.co;2-v","mag":"1990081458"},"language":"en","primary_location":{"id":"doi:10.1002/1099-1506(200010/12)7:7/8<543::aid-nla212>3.0.co;2-v","is_oa":false,"landing_page_url":"https://doi.org/10.1002/1099-1506(200010/12)7:7/8<543::aid-nla212>3.0.co;2-v","pdf_url":null,"source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with 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/A5109536434","display_name":"L. Yu. Kolotilina","orcid":null},"institutions":[{"id":"https://openalex.org/I1313323035","display_name":"Russian Academy of Sciences","ror":"https://ror.org/05qrfxd25","country_code":"RU","type":"funder","lineage":["https://openalex.org/I1313323035"]},{"id":"https://openalex.org/I2801160905","display_name":"Steklov Mathematical Institute","ror":"https://ror.org/03zeg8w71","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I2801160905","https://openalex.org/I4210124601"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"L. Yu. Kolotilina","raw_affiliation_strings":["St.Petersburg Branch of V.A. Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St.Petersburg 191011, Russian Federation","St.Petersburg Branch of V.A. Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191011, Russian Federation"],"affiliations":[{"raw_affiliation_string":"St.Petersburg Branch of V.A. Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St.Petersburg 191011, Russian Federation","institution_ids":["https://openalex.org/I2801160905","https://openalex.org/I1313323035"]},{"raw_affiliation_string":"St.Petersburg Branch of V.A. Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191011, Russian Federation","institution_ids":["https://openalex.org/I2801160905","https://openalex.org/I1313323035"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009508872","display_name":"A. A. Nikishin","orcid":null},"institutions":[{"id":"https://openalex.org/I4210143490","display_name":"Computing Center","ror":"https://ror.org/0557kgc34","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210143490","https://openalex.org/I4210148470"]},{"id":"https://openalex.org/I1313323035","display_name":"Russian Academy of Sciences","ror":"https://ror.org/05qrfxd25","country_code":"RU","type":"funder","lineage":["https://openalex.org/I1313323035"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"A. A. Nikishin","raw_affiliation_strings":["Computing Center for the Russian Academy of Sciences, Vavilov str., 40, Moscow 117967, Russian Federation"],"affiliations":[{"raw_affiliation_string":"Computing Center for the Russian Academy of Sciences, Vavilov str., 40, Moscow 117967, Russian Federation","institution_ids":["https://openalex.org/I4210143490","https://openalex.org/I1313323035"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035303125","display_name":"A. Yu. Yeremin","orcid":null},"institutions":[{"id":"https://openalex.org/I19880235","display_name":"Lomonosov Moscow State University","ror":"https://ror.org/010pmpe69","country_code":"RU","type":"education","lineage":["https://openalex.org/I19880235"]},{"id":"https://openalex.org/I4210159227","display_name":"Institute of Mathematical Problems of Biology","ror":"https://ror.org/04xtpdj18","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210124601","https://openalex.org/I4210159227"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"A. Yu. Yeremin","raw_affiliation_strings":["Research Computing Center for the Moscow State University, Vorobievy Gory, Moscow 119899, Russian Federation"],"affiliations":[{"raw_affiliation_string":"Research Computing Center for the Moscow State University, Vorobievy Gory, Moscow 119899, Russian Federation","institution_ids":["https://openalex.org/I19880235","https://openalex.org/I4210159227"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5009508872","https://openalex.org/A5035303125","https://openalex.org/A5109536434"],"corresponding_institution_ids":["https://openalex.org/I1313323035","https://openalex.org/I19880235","https://openalex.org/I2801160905","https://openalex.org/I4210143490","https://openalex.org/I4210159227"],"apc_list":{"value":4430,"currency":"USD","value_usd":4430},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.11745019,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"7","issue":"7-8","first_page":"543","last_page":"567"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":1.0,"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":1.0,"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":0.996399998664856,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9822999835014343,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/mathematics","display_name":"Mathematics","score":0.7185338139533997},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.6798173189163208},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6110141277313232},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.5650746822357178},{"id":"https://openalex.org/keywords/triangular-matrix","display_name":"Triangular matrix","score":0.541795015335083},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5119420289993286},{"id":"https://openalex.org/keywords/incomplete-lu-factorization","display_name":"Incomplete LU factorization","score":0.42592141032218933},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.4231802821159363},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.345123827457428},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3314974904060364},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.25639575719833374},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.18022441864013672},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.06271475553512573},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.058037757873535156}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7185338139533997},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.6798173189163208},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6110141277313232},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.5650746822357178},{"id":"https://openalex.org/C104528550","wikidata":"https://www.wikidata.org/wiki/Q506265","display_name":"Triangular matrix","level":3,"score":0.541795015335083},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5119420289993286},{"id":"https://openalex.org/C134978465","wikidata":"https://www.wikidata.org/wiki/Q1654069","display_name":"Incomplete LU factorization","level":4,"score":0.42592141032218933},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.4231802821159363},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.345123827457428},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3314974904060364},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.25639575719833374},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.18022441864013672},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.06271475553512573},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.058037757873535156},{"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},{"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/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/1099-1506(200010/12)7:7/8<543::aid-nla212>3.0.co;2-v","is_oa":false,"landing_page_url":"https://doi.org/10.1002/1099-1506(200010/12)7:7/8<543::aid-nla212>3.0.co;2-v","pdf_url":null,"source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with 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":19,"referenced_works":["https://openalex.org/W1500921805","https://openalex.org/W1673003727","https://openalex.org/W1971440257","https://openalex.org/W1977444623","https://openalex.org/W1977631509","https://openalex.org/W1981885118","https://openalex.org/W1985968347","https://openalex.org/W1994805693","https://openalex.org/W2058997431","https://openalex.org/W2082434918","https://openalex.org/W2140153041","https://openalex.org/W2164374667","https://openalex.org/W2569133694","https://openalex.org/W6630034875","https://openalex.org/W6644740676","https://openalex.org/W6656652031","https://openalex.org/W6665626588","https://openalex.org/W6779857112","https://openalex.org/W6990123309"],"related_works":["https://openalex.org/W2164374667","https://openalex.org/W1881162179","https://openalex.org/W2375608986","https://openalex.org/W2095258827","https://openalex.org/W2060455298","https://openalex.org/W4250081984","https://openalex.org/W648090951","https://openalex.org/W1973623209","https://openalex.org/W2065280300","https://openalex.org/W2006502019"],"abstract_inverted_index":{"This":[0,17],"paper":[1],"suggests":[2],"a":[3],"new":[4],"algorithm,":[5],"called":[6],"IBBLU,":[7],"for":[8,65],"constructing":[9],"incomplete":[10],"LU-factorizations":[11],"of":[12,36,56],"general":[13],"non-singular":[14],"sparse":[15,29],"matrices.":[16],"algorithm":[18,60],"is":[19,62,85],"based":[20],"on":[21],"the":[22,34,53,57,73],"block":[23,49],"bordering":[24],"idea":[25],"and":[26,43,67,69,82],"uses":[27],"factorized":[28],"approximate":[30,33],"inverses":[31,35],"to":[32],"pivot":[37],"blocks.":[38],"The":[39,59],"triangular":[40],"factors":[41],"L":[42],"U":[44],"are":[45],"represented":[46],"in":[47,79],"explicit-implicit":[48],"form,":[50],"which":[51],"enhances":[52],"flop":[54],"performance":[55],"preconditioning.":[58],"suggested":[61],"theoretically":[63],"justified":[64],"M-":[66],"H-matrices,":[68],"its":[70],"competitiveness":[71],"with":[72],"best":[74],"available":[75],"algebraic":[76],"preconditioning":[77],"methods":[78],"both":[80],"symmetric":[81],"unsymmetric":[83],"cases":[84],"demonstrated":[86],"numerically.":[87],"Copyright":[88],"\u00a9":[89],"2000":[90],"John":[91],"Wiley":[92],"&":[93],"Sons,":[94],"Ltd.":[95]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}