{"id":"https://openalex.org/W2022844944","doi":"https://doi.org/10.1137/s1064827502408591","title":"A Class of Spectral Two-Level Preconditioners","display_name":"A Class of Spectral Two-Level Preconditioners","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W2022844944","doi":"https://doi.org/10.1137/s1064827502408591","mag":"2022844944"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827502408591","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827502408591","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://research.rug.nl/en/publications/6f8a4d59-a2fa-497b-8023-924f97c93b06","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051748763","display_name":"Bruno Carpentieri","orcid":"https://orcid.org/0000-0002-0516-0033"},"institutions":[{"id":"https://openalex.org/I4210119692","display_name":"Numerical Method (China)","ror":"https://ror.org/02ns8zp42","country_code":"CN","type":"company","lineage":["https://openalex.org/I4210119692"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"B. Carpentieri","raw_affiliation_strings":["Computational and Numerical Mathematics"],"affiliations":[{"raw_affiliation_string":"Computational and Numerical Mathematics","institution_ids":["https://openalex.org/I4210119692"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110062963","display_name":"I. S. Duff","orcid":null},"institutions":[{"id":"https://openalex.org/I1286704778","display_name":"Rutherford Appleton Laboratory","ror":"https://ror.org/03gq8fr08","country_code":"GB","type":"facility","lineage":["https://openalex.org/I1286704778","https://openalex.org/I162524378","https://openalex.org/I4210087105"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"I. S. Duff","raw_affiliation_strings":["Rutherford Appleton Lab, STFC Rutherford Appleton Laboratory"],"affiliations":[{"raw_affiliation_string":"Rutherford Appleton Lab, STFC Rutherford Appleton Laboratory","institution_ids":["https://openalex.org/I1286704778"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060047917","display_name":"Luc Giraud","orcid":"https://orcid.org/0000-0002-7062-7672"},"institutions":[{"id":"https://openalex.org/I4210106946","display_name":"Centre Europ\u00e9en de Recherche et de Formation Avanc\u00e9e en Calcul Scientifique","ror":"https://ror.org/02dzbc556","country_code":"FR","type":"facility","lineage":["https://openalex.org/I4210106946"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"L. Giraud","raw_affiliation_strings":["CERFACS"],"affiliations":[{"raw_affiliation_string":"CERFACS","institution_ids":["https://openalex.org/I4210106946"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5051748763"],"corresponding_institution_ids":["https://openalex.org/I4210119692"],"apc_list":null,"apc_paid":null,"fwci":5.8189,"has_fulltext":false,"cited_by_count":79,"citation_normalized_percentile":{"value":0.96461736,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"25","issue":"2","first_page":"749","last_page":"765"},"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":0.9997000098228455,"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":0.9922000169754028,"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/preconditioner","display_name":"Preconditioner","score":0.9461013078689575},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.763740599155426},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7494770884513855},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.6751555800437927},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5758559107780457},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.5026297569274902},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5016698837280273},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.5000085830688477},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.41289907693862915},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33022481203079224},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2988909184932709},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20567908883094788}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.9461013078689575},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.763740599155426},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7494770884513855},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.6751555800437927},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5758559107780457},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.5026297569274902},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5016698837280273},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.5000085830688477},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.41289907693862915},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33022481203079224},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2988909184932709},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20567908883094788},{"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/s1064827502408591","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827502408591","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:pure.rug.nl:openaire/6f8a4d59-a2fa-497b-8023-924f97c93b06","is_oa":true,"landing_page_url":"https://research.rug.nl/en/publications/6f8a4d59-a2fa-497b-8023-924f97c93b06","pdf_url":null,"source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Carpentieri, B, Duff, I S & Giraud, L 2003, 'A class of spectral two-level preconditioners', SIAM: Journal on Scientific Computing, vol. 25, no. 2, pp. 749\u2013765. https://doi.org/10.1137/S1064827502408591","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:alma.39UBZ_INST:11293113420001241","is_oa":false,"landing_page_url":"https://doi.org/10.1137/S1064827502408591","pdf_url":null,"source":{"id":"https://openalex.org/S4210197018","display_name":"View","issn_l":"2688-268X","issn":["2688-268X","2688-3988"],"is_oa":false,"is_in_doaj":true,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:epubs.cclrc.ac.uk:work/29525","is_oa":false,"landing_page_url":"http://purl.org/net/epubs/work/29525","pdf_url":null,"source":{"id":"https://openalex.org/S4306400334","display_name":"Science and Technology Facilities Council","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},{"id":"pmh:oai:pure.rug.nl:openaire_cris_publications/6f8a4d59-a2fa-497b-8023-924f97c93b06","is_oa":true,"landing_page_url":"https://hdl.handle.net/11370/6f8a4d59-a2fa-497b-8023-924f97c93b06","pdf_url":null,"source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"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":"Carpentieri, B, Duff, I S & Giraud, L 2003, 'A class of spectral two-level preconditioners', SIAM: Journal on Scientific Computing, vol. 25, no. 2, pp. 749\u2013765. https://doi.org/10.1137/S1064827502408591","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:unibz.it:11293113420001241","is_oa":false,"landing_page_url":"https://bia.unibz.it/esploro/outputs/journalArticle/A-class-of-spectral-two-level-preconditioners/991006495382001241","pdf_url":null,"source":{"id":"https://openalex.org/S4210197018","display_name":"View","issn_l":"2688-268X","issn":["2688-268X","2688-3988"],"is_oa":false,"is_in_doaj":true,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:pure.rug.nl:openaire/6f8a4d59-a2fa-497b-8023-924f97c93b06","is_oa":true,"landing_page_url":"https://research.rug.nl/en/publications/6f8a4d59-a2fa-497b-8023-924f97c93b06","pdf_url":null,"source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Carpentieri, B, Duff, I S & Giraud, L 2003, 'A class of spectral two-level preconditioners', SIAM: Journal on Scientific Computing, vol. 25, no. 2, pp. 749\u2013765. https://doi.org/10.1137/S1064827502408591","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1613455162","https://openalex.org/W1974565581","https://openalex.org/W1977061454","https://openalex.org/W1979057228","https://openalex.org/W1990351032","https://openalex.org/W2001068358","https://openalex.org/W2006651457","https://openalex.org/W2009718358","https://openalex.org/W2028989647","https://openalex.org/W2036735300","https://openalex.org/W2044262951","https://openalex.org/W2046160677","https://openalex.org/W2049395862","https://openalex.org/W2050662062","https://openalex.org/W2051133095","https://openalex.org/W2052579356","https://openalex.org/W2067028470","https://openalex.org/W2069262775","https://openalex.org/W2079308547","https://openalex.org/W2088116381","https://openalex.org/W2140153041","https://openalex.org/W2155216327","https://openalex.org/W2164374667","https://openalex.org/W3022136271"],"related_works":["https://openalex.org/W3160810049","https://openalex.org/W2986665254","https://openalex.org/W1994349276","https://openalex.org/W3204470723","https://openalex.org/W1575783825","https://openalex.org/W2096346341","https://openalex.org/W2525981419","https://openalex.org/W3139004046","https://openalex.org/W2890462359","https://openalex.org/W4289542714"],"abstract_inverted_index":{"It":[0],"is":[1,29,159],"well":[2],"known":[3],"that":[4,31,51,104],"the":[5,12,22,33,39,47,70,73,80,87,117,122,128,136,148,155,169,173,180,187,191,210,213,226],"convergence":[6],"of":[7,94,193,203,212],"Krylov":[8,75],"methods":[9],"for":[10,97,100,109,154,215,229],"solving":[11,216],"linear":[13,102,205,218],"system":[14,119,183],"often":[15],"depends":[16],"to":[17,53,134,147,150,152,177,186],"a":[18,92,165,201],"large":[19],"extent":[20],"on":[21,68,200],"eigenvalue":[23],"distribution.":[24],"In":[25,82],"many":[26],"cases,":[27],"it":[28],"observed":[30],"``removing'":[32],"smallest":[34,129],"eigenvalues":[35,130,144,167],"can":[36,60,105],"greatly":[37],"improve":[38],"convergence.":[40],"Several":[41],"techniques":[42],"have":[43],"been":[44],"proposed":[45,58],"in":[46,121,142,221],"past":[48],"few":[49,166],"years":[50],"attempt":[52],"tackle":[54],"this":[55,83,133,230],"problem.":[56],"The":[57],"approaches":[59],"be":[61,107],"split":[62],"into":[63],"two":[64],"main":[65,227],"families":[66],"depending":[67],"whether":[69],"scheme":[71],"enlarges":[72],"generated":[74],"space":[76,125],"or":[77],"adaptively":[78],"updates":[79],"preconditioner.":[81,157],"paper,":[84],"we":[85,208],"follow":[86],"second":[88],"approach":[89],"and":[90,99,131],"propose":[91],"class":[93],"preconditioners":[95,214],"both":[96],"unsymmetric":[98],"symmetric":[101,110],"systems":[103,219],"also":[106],"adapted":[108],"positive":[111],"definite":[112],"problems.":[113],"We":[114,189],"effectively":[115],"solve":[116],"preconditioned":[118,137,182],"exactly":[120],"low":[123],"dimensional":[124],"associated":[126],"with":[127],"use":[132],"update":[135,140],"residual.":[138],"This":[139,158],"results":[141],"shifting":[143],"from":[145],"close":[146,176,185],"origin":[149,170],"near":[151,168],"one":[153,178],"new":[156],"ideal":[160],"when":[161],"there":[162],"are":[163,175],"only":[164],"while":[171],"all":[172],"others":[174],"because":[179],"updated":[181],"becomes":[184],"identity.":[188],"illustrate":[190],"performance":[192],"our":[194],"method":[195],"through":[196],"extensive":[197],"numerical":[198],"experiments":[199],"set":[202],"general":[204],"systems.":[206],"Finally,":[207],"show":[209],"advantages":[211],"dense":[217],"arising":[220],"electromagnetism":[222],"applications,":[223],"which":[224],"were":[225],"motivation":[228],"work.":[231]},"counts_by_year":[{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":8}],"updated_date":"2026-04-15T08:11:43.952461","created_date":"2025-10-10T00:00:00"}