{"id":"https://openalex.org/W2963970762","doi":"https://doi.org/10.1137/16m110486x","title":"Low-Rank Correction Methods for Algebraic Domain Decomposition Preconditioners","display_name":"Low-Rank Correction Methods for Algebraic Domain Decomposition Preconditioners","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2963970762","doi":"https://doi.org/10.1137/16m110486x","mag":"2963970762"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m110486x","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_indexed_in_scopus":true,"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":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.osti.gov/biblio/1438714","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101509235","display_name":"Ruipeng Li","orcid":"https://orcid.org/0000-0003-2802-5763"},"institutions":[{"id":"https://openalex.org/I1282311441","display_name":"Lawrence Livermore National Laboratory","ror":"https://ror.org/041nk4h53","country_code":"US","type":"funder","lineage":["https://openalex.org/I1282311441","https://openalex.org/I1330989302","https://openalex.org/I198811213","https://openalex.org/I4210138311"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Li, Ruipeng","raw_affiliation_strings":["Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)"],"affiliations":[{"raw_affiliation_string":"Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)","institution_ids":["https://openalex.org/I1282311441"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016419713","display_name":"Yousef Saad","orcid":"https://orcid.org/0000-0002-8614-5360"},"institutions":[{"id":"https://openalex.org/I4210101327","display_name":"Twin Cities Orthopedics","ror":"https://ror.org/01en4s460","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I4210101327"]},{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"funder","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Saad, Yousef","raw_affiliation_strings":["Univ. of Minnesota, Twin Cities, MN (United States)"],"affiliations":[{"raw_affiliation_string":"Univ. of Minnesota, Twin Cities, MN (United States)","institution_ids":["https://openalex.org/I4210101327","https://openalex.org/I130238516"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.529,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":25,"citation_normalized_percentile":{"value":0.890302,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":92,"max":93},"biblio":{"volume":"38","issue":"3","first_page":"807","last_page":"828"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9999,"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"}},"topics":[{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9999,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9972,"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/krylov-subspace","display_name":"Krylov subspace","score":0.7553759},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5500742},{"id":"https://openalex.org/keywords/low-rank-approximation","display_name":"Low-rank approximation","score":0.4426871},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.43251392},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.42595896},{"id":"https://openalex.org/keywords/qr-decomposition","display_name":"QR decomposition","score":0.42572415},{"id":"https://openalex.org/keywords/lu-decomposition","display_name":"LU decomposition","score":0.42358842}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.8729059},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.7553759},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6353687},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.632162},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.62622887},{"id":"https://openalex.org/C119256216","wikidata":"https://www.wikidata.org/wiki/Q913012","display_name":"Lanczos resampling","level":3,"score":0.61238164},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.58287203},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.5732256},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5500742},{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.4426871},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.43251392},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.43132758},{"id":"https://openalex.org/C124066611","wikidata":"https://www.wikidata.org/wiki/Q28684319","display_name":"Sparse approximation","level":2,"score":0.42599463},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.42595896},{"id":"https://openalex.org/C188060507","wikidata":"https://www.wikidata.org/wiki/Q653242","display_name":"QR decomposition","level":3,"score":0.42572415},{"id":"https://openalex.org/C123213974","wikidata":"https://www.wikidata.org/wiki/Q833089","display_name":"LU decomposition","level":4,"score":0.42358842},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36557966},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.24259722},{"id":"https://openalex.org/C25023664","wikidata":"https://www.wikidata.org/wiki/Q1575637","display_name":"Hankel matrix","level":2,"score":0.13952458},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.12717557},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.123811156},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.11137855},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.079918444},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m110486x","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_indexed_in_scopus":true,"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":null,"is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/1438714","pdf_url":null,"source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"host_organization_lineage_names":["Office of Scientific and Technical Information"],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/1505.04341","pdf_url":"https://arxiv.org/pdf/1505.04341","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/1438714","pdf_url":null,"source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"host_organization_lineage_names":["Office of Scientific and Technical Information"],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false},"sustainable_development_goals":[],"grants":[{"funder":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation","award_id":"DMS-1216366"},{"funder":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation","award_id":"DMS-1521573"},{"funder":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy","award_id":"DE-AC52-07NA27344 (LLNL-JRNL-727122)"}],"datasets":[],"versions":[],"referenced_works_count":53,"referenced_works":["https://openalex.org/W1492299441","https://openalex.org/W1506342804","https://openalex.org/W1520511539","https://openalex.org/W1547507450","https://openalex.org/W1559275088","https://openalex.org/W1569090332","https://openalex.org/W1569304948","https://openalex.org/W1584657480","https://openalex.org/W1594653673","https://openalex.org/W1712535590","https://openalex.org/W18951224","https://openalex.org/W1965034778","https://openalex.org/W1973786815","https://openalex.org/W1979511352","https://openalex.org/W1981745143","https://openalex.org/W2014168697","https://openalex.org/W2014730252","https://openalex.org/W2018419001","https://openalex.org/W2023567863","https://openalex.org/W2024615455","https://openalex.org/W2026968857","https://openalex.org/W2031528426","https://openalex.org/W2035080386","https://openalex.org/W2035864055","https://openalex.org/W2036564429","https://openalex.org/W2041876368","https://openalex.org/W2049664825","https://openalex.org/W2055373329","https://openalex.org/W2059586807","https://openalex.org/W2070232376","https://openalex.org/W2074093855","https://openalex.org/W2075490698","https://openalex.org/W2078311192","https://openalex.org/W2078645506","https://openalex.org/W2082817855","https://openalex.org/W2084073638","https://openalex.org/W2089958289","https://openalex.org/W2098102734","https://openalex.org/W2101196233","https://openalex.org/W2114030927","https://openalex.org/W2116808829","https://openalex.org/W2117686912","https://openalex.org/W2117756735","https://openalex.org/W2122137889","https://openalex.org/W2141719776","https://openalex.org/W2142184646","https://openalex.org/W2143131337","https://openalex.org/W2188296733","https://openalex.org/W2290288665","https://openalex.org/W25664821","https://openalex.org/W2690223459","https://openalex.org/W2962850972","https://openalex.org/W90568776"],"related_works":["https://openalex.org/W4301683480","https://openalex.org/W4287126381","https://openalex.org/W3201061354","https://openalex.org/W3166616159","https://openalex.org/W2950418232","https://openalex.org/W2889932903","https://openalex.org/W2045998430","https://openalex.org/W1977732568","https://openalex.org/W1964004266","https://openalex.org/W1599640686"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"a":[3,23,47,102],"parallel":[4,104],"preconditioning":[5,63,108],"method":[6],"for":[7,93,112],"distributed":[8,27],"sparse":[9,28,96],"linear":[10,97,117],"systems,":[11],"based":[12],"on":[13],"an":[14],"approximate":[15],"inverse":[16],"of":[17,26,61],"the":[18,42,54,62,71],"original":[19],"matrix,":[20],"that":[21],"adopts":[22],"general":[24],"framework":[25],"matrices":[29],"and":[30,35,91,116],"exploits":[31],"domain":[32],"decomposition":[33],"(DD)":[34],"low-rank":[36,48,66],"corrections.":[37],"The":[38,65],"DD":[39],"approach":[40],"decouples":[41],"matrix":[43],"and,":[44],"once":[45],"inverted,":[46],"approximation":[49],"is":[50,68],"applied":[51],"by":[52,70],"exploiting":[53],"Sherman--Morrison--Woodbury":[55],"formula,":[56],"which":[57],"yields":[58],"two":[59],"variants":[60],"methods.":[64],"expansion":[67],"computed":[69],"Lanczos":[72],"procedure":[73],"with":[74,82,100],"reorthogonalizations.":[75],"Numerical":[76],"experiments":[77],"indicate":[78],"that,":[79],"when":[80],"combined":[81],"Krylov":[83],"subspace":[84],"accelerators,":[85],"this":[86],"preconditioner":[87],"can":[88],"be":[89],"efficient":[90],"robust":[92],"solving":[94,113],"symmetric":[95],"systems.":[98],"Comparisons":[99],"pARMS,":[101],"DD-based":[103],"incomplete":[105],"LU":[106],"(ILU)":[107],"method,":[109],"are":[110],"presented":[111],"Poisson's":[114],"equation":[115],"elasticity":[118],"problems.":[119]},"abstract_inverted_index_v3":null,"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2963970762","counts_by_year":[{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":2}],"updated_date":"2025-03-27T09:25:56.780460","created_date":"2019-07-30"}