{"id":"https://openalex.org/W2804722640","doi":"https://doi.org/10.1137/17m1121226","title":"Iterative Methods for Double Saddle Point Systems","display_name":"Iterative Methods for Double Saddle Point Systems","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2804722640","doi":"https://doi.org/10.1137/17m1121226","mag":"2804722640"},"language":"en","primary_location":{"id":"doi:10.1137/17m1121226","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1121226","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":"https://epubs.siam.org/doi/pdf/10.1137/17M1121226","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060967428","display_name":"Fatemeh Panjeh Ali Beik","orcid":"https://orcid.org/0000-0001-9050-3506"},"institutions":[{"id":"https://openalex.org/I3020488725","display_name":"Vali Asr University of Rafsanjan","ror":"https://ror.org/056xnk046","country_code":"IR","type":"education","lineage":["https://openalex.org/I3020488725"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Fatemeh Panjeh Ali Beik","raw_affiliation_strings":["Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran","institution_ids":["https://openalex.org/I3020488725"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053109099","display_name":"Michele Benzi","orcid":"https://orcid.org/0000-0001-6099-0294"},"institutions":[{"id":"https://openalex.org/I150468666","display_name":"Emory University","ror":"https://ror.org/03czfpz43","country_code":"US","type":"education","lineage":["https://openalex.org/I150468666"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Michele Benzi","raw_affiliation_strings":["Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322","institution_ids":["https://openalex.org/I150468666"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.0058,"has_fulltext":false,"cited_by_count":76,"citation_normalized_percentile":{"value":0.96938546,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"39","issue":"2","first_page":"902","last_page":"921"},"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":0.9994000196456909,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.8362741470336914},{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.8220643997192383},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8024512529373169},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.6281701922416687},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5881489515304565},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5866449475288391},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.5377907752990723},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5243057012557983},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.4977553188800812},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.4338324964046478},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.42043739557266235},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3060374855995178},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.301830530166626},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.16574153304100037},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15573498606681824}],"concepts":[{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.8362741470336914},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.8220643997192383},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8024512529373169},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.6281701922416687},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5881489515304565},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5866449475288391},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.5377907752990723},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5243057012557983},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.4977553188800812},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.4338324964046478},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.42043739557266235},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3060374855995178},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.301830530166626},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.16574153304100037},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15573498606681824},{"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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/17m1121226","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1121226","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:ricerca.sns.it:11384/75272","is_oa":true,"landing_page_url":"https://epubs.siam.org/doi/pdf/10.1137/17M1121226","pdf_url":null,"source":{"id":"https://openalex.org/S7407050981","display_name":"Scuola Normale Superiore di Pisa","issn_l":null,"issn":[],"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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:ricerca.sns.it:11384/75272","is_oa":true,"landing_page_url":"https://epubs.siam.org/doi/pdf/10.1137/17M1121226","pdf_url":null,"source":{"id":"https://openalex.org/S7407050981","display_name":"Scuola Normale Superiore di Pisa","issn_l":null,"issn":[],"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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3482081272","display_name":null,"funder_award_id":"DMS-1418889","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1506342804","https://openalex.org/W1673742782","https://openalex.org/W1875770540","https://openalex.org/W1981220107","https://openalex.org/W2015295891","https://openalex.org/W2018850201","https://openalex.org/W2024396817","https://openalex.org/W2034234432","https://openalex.org/W2050206349","https://openalex.org/W2056828987","https://openalex.org/W2067313886","https://openalex.org/W2080421693","https://openalex.org/W2089558316","https://openalex.org/W2128132991","https://openalex.org/W2141870784","https://openalex.org/W2223789773","https://openalex.org/W2288526001","https://openalex.org/W2463887153","https://openalex.org/W2604122689","https://openalex.org/W2610857016","https://openalex.org/W3100426362"],"related_works":["https://openalex.org/W2401310550","https://openalex.org/W2381322109","https://openalex.org/W1189497506","https://openalex.org/W3146410598","https://openalex.org/W2767153625","https://openalex.org/W1970706285","https://openalex.org/W1982069796","https://openalex.org/W3046775784","https://openalex.org/W3031624508","https://openalex.org/W2604862712"],"abstract_inverted_index":{"We":[0,27],"consider":[1],"the":[2,32,50,56],"iterative":[3],"solution":[4],"of":[5,8,34,40,58],"a":[6],"class":[7],"linear":[9],"systems":[10],"with":[11],"double":[12],"saddle":[13],"point":[14],"structure.":[15],"Several":[16],"block":[17],"preconditioners":[18],"for":[19,31],"Krylov":[20],"subspace":[21],"methods":[22],"are":[23],"described":[24],"and":[25,37,55],"analyzed.":[26],"derive":[28],"some":[29],"bounds":[30],"eigenvalues":[33],"preconditioned":[35],"matrices":[36],"present":[38],"results":[39],"numerical":[41],"experiments":[42],"using":[43],"test":[44],"problems":[45],"from":[46],"two":[47],"different":[48],"applications:":[49],"potential":[51],"fluid":[52],"flow":[53],"problem":[54],"modeling":[57],"liquid":[59],"crystals":[60],"directors.":[61]},"counts_by_year":[{"year":2026,"cited_by_count":9},{"year":2025,"cited_by_count":12},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":14},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}