{"id":"https://openalex.org/W1556679496","doi":"https://doi.org/10.1137/15m1031539","title":"Algebraic Two-Level Convergence Theory for Singular Systems","display_name":"Algebraic Two-Level Convergence Theory for Singular Systems","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W1556679496","doi":"https://doi.org/10.1137/15m1031539","mag":"1556679496"},"language":"en","primary_location":{"id":"doi:10.1137/15m1031539","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1031539","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":true,"oa_status":"green","oa_url":"http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/208276","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057146535","display_name":"Yvan Notay","orcid":"https://orcid.org/0000-0001-7176-4890"},"institutions":[{"id":"https://openalex.org/I132053463","display_name":"Universit\u00e9 Libre de Bruxelles","ror":"https://ror.org/01r9htc13","country_code":"BE","type":"education","lineage":["https://openalex.org/I132053463"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"Yvan Notay","raw_affiliation_strings":["Universit\u00e9 libre de Bruxelles"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 libre de Bruxelles","institution_ids":["https://openalex.org/I132053463"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5057146535"],"corresponding_institution_ids":["https://openalex.org/I132053463"],"apc_list":null,"apc_paid":null,"fwci":1.8515,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.82631284,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"37","issue":"4","first_page":"1419","last_page":"1439"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9983999729156494,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9965000152587891,"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/mathematics","display_name":"Mathematics","score":0.8794927597045898},{"id":"https://openalex.org/keywords/singular-point-of-an-algebraic-variety","display_name":"Singular point of an algebraic variety","score":0.6707295775413513},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5917635560035706},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5709657073020935},{"id":"https://openalex.org/keywords/symbolic-convergence-theory","display_name":"Symbolic convergence theory","score":0.5643585324287415},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4952367842197418},{"id":"https://openalex.org/keywords/algebraic-geometry","display_name":"Algebraic geometry","score":0.4580911099910736},{"id":"https://openalex.org/keywords/algebraic-theory","display_name":"Algebraic theory","score":0.4461211860179901},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4201708734035492},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3481580317020416},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32344770431518555},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.10572603344917297},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.09404963254928589}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8794927597045898},{"id":"https://openalex.org/C201482947","wikidata":"https://www.wikidata.org/wiki/Q7524253","display_name":"Singular point of an algebraic variety","level":5,"score":0.6707295775413513},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5917635560035706},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5709657073020935},{"id":"https://openalex.org/C64980692","wikidata":"https://www.wikidata.org/wiki/Q16191959","display_name":"Symbolic convergence theory","level":3,"score":0.5643585324287415},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4952367842197418},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.4580911099910736},{"id":"https://openalex.org/C2779782106","wikidata":"https://www.wikidata.org/wiki/Q4724020","display_name":"Algebraic theory","level":3,"score":0.4461211860179901},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4201708734035492},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3481580317020416},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32344770431518555},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.10572603344917297},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.09404963254928589},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/15m1031539","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1031539","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:10.1.1.696.2021","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.696.2021","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://homepages.ulb.ac.be/%7Eynotay/PDF/ganmn1501.pdf","raw_type":"text"},{"id":"pmh:oai:dipot.ulb.ac.be:2013/208276","is_oa":true,"landing_page_url":"http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/208276","pdf_url":null,"source":{"id":"https://openalex.org/S4306401063","display_name":"D\u00e9p\u00f4t institutionnel de l'Universit\u00e9 libre de Bruxelles (Universit\u00e9 Libre de Bruxelles)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I132053463","host_organization_name":"Universit\u00e9 Libre de Bruxelles","host_organization_lineage":["https://openalex.org/I132053463"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM journal on matrix analysis and applications, 37","raw_type":"info:ulb-repo/semantics/openurl/article"},{"id":"pmh:oai:dipot.ulb.ac.be:2013/247753","is_oa":false,"landing_page_url":"http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/247753","pdf_url":null,"source":{"id":"https://openalex.org/S4306401063","display_name":"D\u00e9p\u00f4t institutionnel de l'Universit\u00e9 libre de Bruxelles (Universit\u00e9 Libre de Bruxelles)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I132053463","host_organization_name":"Universit\u00e9 Libre de Bruxelles","host_organization_lineage":["https://openalex.org/I132053463"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM journal on matrix analysis and applications, 37 (4","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:dipot.ulb.ac.be:2013/208276","is_oa":true,"landing_page_url":"http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/208276","pdf_url":null,"source":{"id":"https://openalex.org/S4306401063","display_name":"D\u00e9p\u00f4t institutionnel de l'Universit\u00e9 libre de Bruxelles (Universit\u00e9 Libre de Bruxelles)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I132053463","host_organization_name":"Universit\u00e9 Libre de Bruxelles","host_organization_lineage":["https://openalex.org/I132053463"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM journal on matrix analysis and applications, 37","raw_type":"info:ulb-repo/semantics/openurl/article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321390","display_name":"Fonds De La Recherche Scientifique - FNRS","ror":"https://ror.org/03q83t159"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W1519509134","https://openalex.org/W1542243431","https://openalex.org/W1636009176","https://openalex.org/W1806777346","https://openalex.org/W1961194538","https://openalex.org/W1980500205","https://openalex.org/W1981142209","https://openalex.org/W1984747903","https://openalex.org/W1994183034","https://openalex.org/W2001415695","https://openalex.org/W2006401637","https://openalex.org/W2006895912","https://openalex.org/W2009250131","https://openalex.org/W2012349161","https://openalex.org/W2019212238","https://openalex.org/W2021491994","https://openalex.org/W2040050796","https://openalex.org/W2041257655","https://openalex.org/W2047714674","https://openalex.org/W2048803822","https://openalex.org/W2050711087","https://openalex.org/W2055576996","https://openalex.org/W2062618977","https://openalex.org/W2064878022","https://openalex.org/W2067941796","https://openalex.org/W2070448527","https://openalex.org/W2071700284","https://openalex.org/W2075536798","https://openalex.org/W2078687549","https://openalex.org/W2084526231","https://openalex.org/W2094626027","https://openalex.org/W2098217482","https://openalex.org/W2106088594","https://openalex.org/W2119862562","https://openalex.org/W2128038070","https://openalex.org/W2128328239","https://openalex.org/W2130641059","https://openalex.org/W2137788339","https://openalex.org/W2140202900","https://openalex.org/W2142846929","https://openalex.org/W2157875412","https://openalex.org/W2166360652","https://openalex.org/W2170392325","https://openalex.org/W2610857016","https://openalex.org/W2914105805"],"related_works":["https://openalex.org/W2615709397","https://openalex.org/W4301268047","https://openalex.org/W2949562154","https://openalex.org/W1989039217","https://openalex.org/W2055765740","https://openalex.org/W4238420390","https://openalex.org/W4240813704","https://openalex.org/W1603772710","https://openalex.org/W2024069909","https://openalex.org/W1556679496"],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,17,22,32,51,81,104,107,110,113,129,140],"algebraic":[3,13],"convergence":[4,35],"theory":[5],"that":[6,128],"gives":[7],"its":[8],"theoretical":[9],"foundations":[10],"to":[11,27,50,109],"classical":[12],"multigrid":[14],"methods.":[15],"All":[16],"main":[18],"results":[19,46,83],"constitutive":[20],"of":[21,66,106,131],"approach":[23],"are":[24],"properly":[25],"extended":[26],"singular":[28,52,70,141],"compatible":[29],"systems,":[30],"including":[31],"recent":[33],"sharp":[34],"estimates":[36],"for":[37,118,139,146],"both":[38],"symmetric":[39],"and":[40],"nonsymmetric":[41],"systems.":[42],"In":[43],"fact,":[44],"all":[45],"carry":[47],"over":[48],"smoothly":[49],"case,":[53],"which":[54],"therefore":[55],"does":[56],"not":[57],"require":[58],"a":[59,63,77,93],"specific":[60],"treatment":[61],"(except":[62],"proper":[64],"handling":[65],"issues":[67],"associated":[68],"with":[69,76,120],"coarse":[71],"grid":[72],"matrices).":[73],"Regarding":[74],"problems":[75,119],"low-dimensional":[78],"null":[79,122],"space,":[80],"presented":[82],"thus":[84],"mainly":[85],"confirm":[86],"what":[87],"has":[88],"been":[89],"observed":[90],"often":[91],"at":[92],"more":[94],"practical":[95],"level":[96],"in":[97],"many":[98],"previous":[99],"works.":[100],"As":[101],"illustrated":[102],"by":[103],"discussion":[105],"application":[108],"curl-curl":[111],"equation,":[112],"potential":[114],"impact":[115],"is":[116,145],"greater":[117],"large-dimensional":[121],"space.":[123],"Indeed,":[124],"it":[125,144],"turns":[126],"out":[127],"design":[130],"multilevel":[132],"methods":[133],"can":[134],"then":[135],"actually":[136],"be":[137],"easier":[138],"case":[142],"than":[143],"nearby":[147],"regularized":[148],"problems.":[149]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1}],"updated_date":"2026-04-19T08:26:33.389920","created_date":"2025-10-10T00:00:00"}