{"id":"https://openalex.org/W2154824870","doi":"https://doi.org/10.1137/140978843","title":"Convergence analysis of the Generalized Empirical Interpolation Method","display_name":"Convergence analysis of the Generalized Empirical Interpolation Method","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2154824870","doi":"https://doi.org/10.1137/140978843","mag":"2154824870"},"language":"en","primary_location":{"id":"doi:10.1137/140978843","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140978843","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1605.07730","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Y. Maday","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Y. Maday","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"O. Mula","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"O. Mula","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"G. Turinici","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"G. Turinici","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.2179,"has_fulltext":false,"cited_by_count":45,"citation_normalized_percentile":{"value":0.9327099,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"54","issue":"3","first_page":"1713","last_page":"1731"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.3580999970436096,"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"}},"topics":[{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.3580999970436096,"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"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.0737999975681305,"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/T11545","display_name":"Advanced Banach Space Theory","score":0.06499999761581421,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/interpolation","display_name":"Interpolation (computer graphics)","score":0.6523000001907349},{"id":"https://openalex.org/keywords/nearest-neighbor-interpolation","display_name":"Nearest-neighbor interpolation","score":0.5746999979019165},{"id":"https://openalex.org/keywords/polynomial-interpolation","display_name":"Polynomial interpolation","score":0.5623999834060669},{"id":"https://openalex.org/keywords/linear-interpolation","display_name":"Linear interpolation","score":0.5447999835014343},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.5026999711990356},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.47099998593330383},{"id":"https://openalex.org/keywords/birkhoff-interpolation","display_name":"Birkhoff interpolation","score":0.4693000018596649},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.4596000015735626},{"id":"https://openalex.org/keywords/spline-interpolation","display_name":"Spline interpolation","score":0.45509999990463257}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8765000104904175},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.6523000001907349},{"id":"https://openalex.org/C207214200","wikidata":"https://www.wikidata.org/wiki/Q4202129","display_name":"Nearest-neighbor interpolation","level":4,"score":0.5746999979019165},{"id":"https://openalex.org/C88080468","wikidata":"https://www.wikidata.org/wiki/Q637347","display_name":"Polynomial interpolation","level":4,"score":0.5623999834060669},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.5447999835014343},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5159000158309937},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.5026999711990356},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.47099998593330383},{"id":"https://openalex.org/C205280321","wikidata":"https://www.wikidata.org/wiki/Q3800523","display_name":"Birkhoff interpolation","level":5,"score":0.4693000018596649},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.4596000015735626},{"id":"https://openalex.org/C31447003","wikidata":"https://www.wikidata.org/wiki/Q545002","display_name":"Spline interpolation","level":3,"score":0.45509999990463257},{"id":"https://openalex.org/C188325010","wikidata":"https://www.wikidata.org/wiki/Q861176","display_name":"Trilinear interpolation","level":4,"score":0.423799991607666},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4187000095844269},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.40619999170303345},{"id":"https://openalex.org/C28537468","wikidata":"https://www.wikidata.org/wiki/Q464356","display_name":"Trigonometric interpolation","level":5,"score":0.37689998745918274},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3686999976634979},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.36550000309944153},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.36469998955726624},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.3472999930381775},{"id":"https://openalex.org/C119768884","wikidata":"https://www.wikidata.org/wiki/Q7597108","display_name":"Stairstep interpolation","level":4,"score":0.34139999747276306},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3393000066280365},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.31529998779296875},{"id":"https://openalex.org/C143542097","wikidata":"https://www.wikidata.org/wiki/Q3153554","display_name":"Inverse quadratic interpolation","level":5,"score":0.2928999960422516},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2919999957084656},{"id":"https://openalex.org/C142730499","wikidata":"https://www.wikidata.org/wiki/Q934367","display_name":"Function space","level":2,"score":0.28049999475479126},{"id":"https://openalex.org/C6183050","wikidata":"https://www.wikidata.org/wiki/Q3058180","display_name":"Interpolation space","level":4,"score":0.28040000796318054},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2741999924182892},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.27399998903274536},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.2678999900817871},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.2671999931335449},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.25859999656677246}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/140978843","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140978843","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1605.07730","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1605.07730","pdf_url":"https://arxiv.org/pdf/1605.07730","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":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":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-01032458v2","is_oa":true,"landing_page_url":"https://hal.sorbonne-universite.fr/hal-01032458","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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 Numerical Analysis, 2016, 54 (3), pp.1713-1731. ⟨10.1137/140978843⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1605.07730","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1605.07730","pdf_url":"https://arxiv.org/pdf/1605.07730","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":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":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1826439926","https://openalex.org/W1969080915","https://openalex.org/W1995835881","https://openalex.org/W2004587738","https://openalex.org/W2039055345","https://openalex.org/W2047591100","https://openalex.org/W2047942408","https://openalex.org/W2101121254","https://openalex.org/W2107699930","https://openalex.org/W2168970443"],"related_works":[],"abstract_inverted_index":{"Let":[0],"$F$":[1,68,79,124],"be":[2],"a":[3,7,21,61,90,164],"compact":[4],"set":[5],"of":[6,40,53,78,123,134,149],"Banach":[8],"space":[9,52,56],"$\\mathcal{X}$.":[10,54],"This":[11],"paper":[12],"analyzes":[13],"the":[14,38,50,70,85,99,110,120,139,143,147,150,158],"\u201cgeneralized":[15],"empirical":[16],"interpolation":[17,100,140,151],"method,\u201d":[18],"which,":[19],"given":[20],"function":[22],"$f\\in":[23],"F$,":[24],"builds":[25],"an":[26,30,115],"interpolant":[27],"$\\mathcal{J}_n[f]$":[28],"in":[29,69,125,157],"$n$":[31,41,116],"dimensional":[32,117],"subspace":[33],"$X_n":[34],"\\subset":[35],"\\mathcal{X}$":[36],"with":[37,60,109],"knowledge":[39],"outputs":[42],"$(\\sigma_i(f))_{i=1}^n$,":[43],"where":[44,160],"$\\sigma_i\\in":[45],"\\mathcal{X}'$":[46],"and":[47],"$\\mathcal{X}'$":[48],"is":[49,58,65,74,163],"dual":[51],"The":[55,81],"$X_n$":[57],"built":[59],"greedy":[62],"algorithm":[63,82],"that":[64,72,138],"adapted":[66],"to":[67],"sense":[71],"it":[73,108],"generated":[75],"by":[76,106],"elements":[77],"itself.":[80],"also":[83],"selects":[84],"linear":[86],"functionals":[87],"$(\\sigma_i)_{i=1}^n$":[88],"from":[89],"dictionary":[91],"$\\Sigma\\subset":[92],"\\mathcal{X}'$.":[93],"In":[94],"this":[95],"paper,":[96],"we":[97,136],"study":[98],"error":[101,141],"$\\max_{f\\in":[102],"F}":[103],"\\Vert":[104],"f-\\mathcal{J}_n[f]\\Vert_{\\mathcal{X}}$":[105],"comparing":[107],"best":[111],"possible":[112],"performance":[113],"on":[114],"space,":[118],"i.e.,":[119],"Kolmogorov":[121],"$n$-width":[122],"$\\mathcal{X}$,":[126],"$d_n(F,\\mathcal{X})$.":[127],"For":[128],"polynomial":[129],"or":[130],"exponential":[131],"decay":[132],"rates":[133],"$d_n(F,\\mathcal{X})$,":[135],"prove":[137],"has":[142],"same":[144],"behavior":[145],"modulo":[146],"norm":[148],"operator.":[152],"Sharper":[153],"results":[154],"are":[155],"obtained":[156],"case":[159],"$\\mathcal":[161],"X$":[162],"Hilbert":[165],"space.":[166]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":10},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3}],"updated_date":"2026-03-12T08:34:05.389933","created_date":"2016-06-24T00:00:00"}