{"id":"https://openalex.org/W4323361003","doi":"https://doi.org/10.1007/s10444-023-10021-7","title":"Exponential tractability of L2-approximation with function values","display_name":"Exponential tractability of L2-approximation with function values","publication_year":2023,"publication_date":"2023-03-07","ids":{"openalex":"https://openalex.org/W4323361003","doi":"https://doi.org/10.1007/s10444-023-10021-7"},"language":"en","primary_location":{"id":"doi:10.1007/s10444-023-10021-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10444-023-10021-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10444-023-10021-7.pdf","source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10444-023-10021-7.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070459947","display_name":"David Krieg","orcid":"https://orcid.org/0000-0001-8180-8906"},"institutions":[{"id":"https://openalex.org/I121883995","display_name":"Johannes Kepler University of Linz","ror":"https://ror.org/052r2xn60","country_code":"AT","type":"education","lineage":["https://openalex.org/I121883995"]},{"id":"https://openalex.org/I138211613","display_name":"Austrian Academy of Sciences","ror":"https://ror.org/03anc3s24","country_code":"AT","type":"government","lineage":["https://openalex.org/I138211613"]},{"id":"https://openalex.org/I4210158379","display_name":"Johann Radon Institute for Computational and Applied Mathematics","ror":"https://ror.org/05a94k872","country_code":"AT","type":"facility","lineage":["https://openalex.org/I138211613","https://openalex.org/I4210158379"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"David Krieg","raw_affiliation_strings":["Institut f\u00fcr Analysis, Johannes Kepler Universit\u00e4t, Linz, Austria","Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Linz, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Analysis, Johannes Kepler Universit\u00e4t, Linz, Austria","institution_ids":["https://openalex.org/I121883995"]},{"raw_affiliation_string":"Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Linz, Austria","institution_ids":["https://openalex.org/I4210158379","https://openalex.org/I138211613"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005361723","display_name":"Pawe\u0142 Siedlecki","orcid":"https://orcid.org/0000-0001-7352-9253"},"institutions":[{"id":"https://openalex.org/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Pawe\u0142 Siedlecki","raw_affiliation_strings":["Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland"],"raw_orcid":"https://orcid.org/0000-0001-7352-9253","affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland","institution_ids":["https://openalex.org/I4654613"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088907596","display_name":"Mario Ullrich","orcid":null},"institutions":[{"id":"https://openalex.org/I121883995","display_name":"Johannes Kepler University of Linz","ror":"https://ror.org/052r2xn60","country_code":"AT","type":"education","lineage":["https://openalex.org/I121883995"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Mario Ullrich","raw_affiliation_strings":["Institut f\u00fcr Analysis, Johannes Kepler Universit\u00e4t, Linz, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Analysis, Johannes Kepler Universit\u00e4t, Linz, Austria","institution_ids":["https://openalex.org/I121883995"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113930193","display_name":"Henryk Wo\u017aniakowski","orcid":null},"institutions":[{"id":"https://openalex.org/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]},{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["PL","US"],"is_corresponding":false,"raw_author_name":"Henryk Wo\u017aniakowski","raw_affiliation_strings":["Department of Computer Science, Columbia University, New York, USA","Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Columbia University, New York, USA","institution_ids":["https://openalex.org/I78577930"]},{"raw_affiliation_string":"Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland","institution_ids":["https://openalex.org/I4654613"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5070459947"],"corresponding_institution_ids":["https://openalex.org/I121883995","https://openalex.org/I138211613","https://openalex.org/I4210158379"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":3.9826,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.94238477,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"49","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9998000264167786,"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9998000264167786,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9987000226974487,"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":0.998199999332428,"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/mathematics","display_name":"Mathematics","score":0.7210368514060974},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.7033825516700745},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.657293975353241},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5939434766769409},{"id":"https://openalex.org/keywords/approximation-error","display_name":"Approximation error","score":0.5828145742416382},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.559723436832428},{"id":"https://openalex.org/keywords/linear-approximation","display_name":"Linear approximation","score":0.49069154262542725},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.46332401037216187},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45232802629470825},{"id":"https://openalex.org/keywords/function-approximation","display_name":"Function approximation","score":0.4395048916339874},{"id":"https://openalex.org/keywords/exponential-growth","display_name":"Exponential growth","score":0.424178808927536},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.41111040115356445},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35120242834091187},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.29227131605148315},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21140778064727783},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21040421724319458},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.09325265884399414},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.06571125984191895},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06256386637687683}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7210368514060974},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.7033825516700745},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.657293975353241},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5939434766769409},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.5828145742416382},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.559723436832428},{"id":"https://openalex.org/C160824197","wikidata":"https://www.wikidata.org/wiki/Q2071054","display_name":"Linear approximation","level":3,"score":0.49069154262542725},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.46332401037216187},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45232802629470825},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.4395048916339874},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.424178808927536},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.41111040115356445},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35120242834091187},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.29227131605148315},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21140778064727783},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21040421724319458},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.09325265884399414},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.06571125984191895},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06256386637687683},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"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},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10444-023-10021-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10444-023-10021-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10444-023-10021-7.pdf","source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s10444-023-10021-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10444-023-10021-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10444-023-10021-7.pdf","source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G378720623","display_name":null,"funder_award_id":"F5506","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4323361003.pdf"},"referenced_works_count":44,"referenced_works":["https://openalex.org/W1820164671","https://openalex.org/W1934971259","https://openalex.org/W1974621481","https://openalex.org/W1978653679","https://openalex.org/W2021958990","https://openalex.org/W2030435498","https://openalex.org/W2039055345","https://openalex.org/W2049196399","https://openalex.org/W2049211937","https://openalex.org/W2049536068","https://openalex.org/W2067507602","https://openalex.org/W2075646404","https://openalex.org/W2085335060","https://openalex.org/W2113499611","https://openalex.org/W2122080931","https://openalex.org/W2132221321","https://openalex.org/W2142810139","https://openalex.org/W2299627974","https://openalex.org/W2300951034","https://openalex.org/W2323386796","https://openalex.org/W2482752784","https://openalex.org/W2497677836","https://openalex.org/W2767507454","https://openalex.org/W2797465556","https://openalex.org/W2894882666","https://openalex.org/W2900195490","https://openalex.org/W2962718855","https://openalex.org/W2963813846","https://openalex.org/W2964343121","https://openalex.org/W3009724674","https://openalex.org/W3015889624","https://openalex.org/W3017325642","https://openalex.org/W3099181605","https://openalex.org/W3101623935","https://openalex.org/W3102262919","https://openalex.org/W3106024057","https://openalex.org/W3110719148","https://openalex.org/W3110811957","https://openalex.org/W3155210892","https://openalex.org/W3155724638","https://openalex.org/W3158843505","https://openalex.org/W3178042296","https://openalex.org/W3180748791","https://openalex.org/W4311465473"],"related_works":["https://openalex.org/W2087686193","https://openalex.org/W3113145869","https://openalex.org/W3177870706","https://openalex.org/W2097120783","https://openalex.org/W2160821628","https://openalex.org/W2768028474","https://openalex.org/W4239251873","https://openalex.org/W3089181838","https://openalex.org/W2073744204","https://openalex.org/W2096450101"],"abstract_inverted_index":{"Abstract":[0],"We":[1,115],"study":[2],"the":[3,9,22,28,38,41,82,96,102,108,111,120],"complexity":[4],"of":[5,16,24,30,43,79,81,123,133,161,168],"high-dimensional":[6,97],"approximation":[7,83,98],"in":[8,54,88,141],"L":[10],"2":[11],"-norm":[12],"when":[13,40],"different":[14],"classes":[15],"information":[17,124],"are":[18],"available;":[19],"we":[20,36,127,144,150],"compare":[21],"power":[23,29],"function":[25,130],"evaluations":[26],"with":[27],"arbitrary":[31,134],"continuous":[32],"linear":[33,44,135,155],"measurements.":[34],"Here,":[35],"discuss":[37],"situation":[39],"number":[42],"measurements":[45],"required":[46,121],"to":[47,75,117,154],"achieve":[48],"an":[49,76],"error":[50],"\u03b5":[51,69],"\u2208":[52],"(0,1)":[53],"dimension":[55,112],"$d\\in":[56],"\\mathbb":[57],"{N}$":[58],"<mml:math":[59],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[60],"<mml:mi>d</mml:mi>":[61],"<mml:mo>\u2208</mml:mo>":[62],"<mml:mi>\u2115</mml:mi>":[63],"</mml:math>":[64],"depends":[65],"only":[66,129,145],"poly-logarithmically":[67],"on":[68,110],"\u2212":[70],"1":[71],".":[72,114],"This":[73],"corresponds":[74],"exponential":[77],"order":[78],"convergence":[80],"error,":[84],"which":[85,118],"often":[86],"happens":[87],"applications.":[89],"However,":[90],"it":[91],"does":[92],"not":[93],"mean":[94],"that":[95,140],"problem":[99],"is":[100],"easy,":[101],"main":[103],"difficulty":[104],"usually":[105],"lies":[106],"within":[107],"dependence":[109],"d":[113],"determine":[116],"extent":[119],"amount":[122],"changes":[125],"if":[126],"allow":[128],"evaluation":[131],"instead":[132],"information.":[136,170],"It":[137],"turns":[138],"out":[139],"this":[142],"case":[143],"lose":[146],"very":[147],"little,":[148],"and":[149],"can":[151],"even":[152],"restrict":[153],"algorithms.":[156],"In":[157],"particular,":[158],"several":[159],"notions":[160],"tractability":[162],"hold":[163],"simultaneously":[164],"for":[165],"both":[166],"types":[167],"available":[169]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3}],"updated_date":"2026-01-20T23:28:44.954186","created_date":"2025-10-10T00:00:00"}