{"id":"https://openalex.org/W2037562833","doi":"https://doi.org/10.1090/s0025-5718-2013-02759-7","title":"Average case tractability of approximating \u221e-variate functions","display_name":"Average case tractability of approximating \u221e-variate functions","publication_year":2013,"publication_date":"2013-08-01","ids":{"openalex":"https://openalex.org/W2037562833","doi":"https://doi.org/10.1090/s0025-5718-2013-02759-7","mag":"2037562833"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-2013-02759-7","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2013-02759-7","pdf_url":"https://www.ams.org/mcom/2014-83-287/S0025-5718-2013-02759-7/S0025-5718-2013-02759-7.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2014-83-287/S0025-5718-2013-02759-7/S0025-5718-2013-02759-7.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5108821523","display_name":"G.W. Wasilkowski","orcid":null},"institutions":[{"id":"https://openalex.org/I143302722","display_name":"University of Kentucky","ror":"https://ror.org/02k3smh20","country_code":"US","type":"education","lineage":["https://openalex.org/I143302722"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"G. Wasilkowski","raw_affiliation_strings":["Department of Computer Science, University of Kentucky, Lexington, Kentucky 40506"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Kentucky, Lexington, Kentucky 40506","institution_ids":["https://openalex.org/I143302722"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5108821523"],"corresponding_institution_ids":["https://openalex.org/I143302722"],"apc_list":null,"apc_paid":null,"fwci":3.7606,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.92575453,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"83","issue":"287","first_page":"1319","last_page":"1336"},"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9824000000953674,"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/algorithm","display_name":"Algorithm","score":0.576541006565094},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.556165337562561},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5334396958351135},{"id":"https://openalex.org/keywords/tensor-product","display_name":"Tensor product","score":0.5314582586288452},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.5073198676109314},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.49172642827033997},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36006855964660645},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.14935767650604248},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10303390026092529}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.576541006565094},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.556165337562561},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5334396958351135},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.5314582586288452},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.5073198676109314},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.49172642827033997},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36006855964660645},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.14935767650604248},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10303390026092529},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/s0025-5718-2013-02759-7","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2013-02759-7","pdf_url":"https://www.ams.org/mcom/2014-83-287/S0025-5718-2013-02759-7/S0025-5718-2013-02759-7.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-2013-02759-7","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2013-02759-7","pdf_url":"https://www.ams.org/mcom/2014-83-287/S0025-5718-2013-02759-7/S0025-5718-2013-02759-7.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2037562833.pdf","grobid_xml":"https://content.openalex.org/works/W2037562833.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W113936797","https://openalex.org/W167192022","https://openalex.org/W299937665","https://openalex.org/W569564947","https://openalex.org/W1552736770","https://openalex.org/W1569918587","https://openalex.org/W1590281894","https://openalex.org/W1820164671","https://openalex.org/W1966269993","https://openalex.org/W1966589908","https://openalex.org/W1980651498","https://openalex.org/W1983156129","https://openalex.org/W1984812257","https://openalex.org/W2011665537","https://openalex.org/W2017309389","https://openalex.org/W2027915600","https://openalex.org/W2033791986","https://openalex.org/W2044203216","https://openalex.org/W2048357906","https://openalex.org/W2048932584","https://openalex.org/W2067683041","https://openalex.org/W2070190615","https://openalex.org/W2083845086","https://openalex.org/W2091096196","https://openalex.org/W2098612888","https://openalex.org/W2100179204","https://openalex.org/W2125886176","https://openalex.org/W2137224975","https://openalex.org/W2149958429","https://openalex.org/W2203324204","https://openalex.org/W2480987681","https://openalex.org/W2494568668","https://openalex.org/W2497677836","https://openalex.org/W2685500084","https://openalex.org/W3119524009","https://openalex.org/W4241273613","https://openalex.org/W4285719527","https://openalex.org/W4298236820","https://openalex.org/W4300048442"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2467119940","https://openalex.org/W3194077685","https://openalex.org/W2152758797","https://openalex.org/W2382762871","https://openalex.org/W2544423928","https://openalex.org/W2950599922","https://openalex.org/W2327230097","https://openalex.org/W2596950579"],"abstract_inverted_index":{"We":[0,78],"study":[1],"function":[2,59,117,178,193],"approximation":[3,104,179],"in":[4,122,182],"the":[5,56,63,86,94,98,103,116,123],"average":[6],"case":[7,176],"setting":[8],"for":[9,85,143,154],"spaces":[10],"of":[11,58,65,97,125,177],"<inline-formula":[12,156],"content-type=\"math/mathml\">":[13,157],"<mml:math":[14,158],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[15,159],"alttext=\"normal":[16],"infinity\">":[17],"<mml:semantics>":[18,163],"<mml:mi":[19],"mathvariant=\"normal\">":[20],"\u221e":[21],"</mml:mi>":[22],"<mml:annotation":[23,168],"encoding=\"application/x-tex\">\\infty</mml:annotation>":[24],"</mml:semantics>":[25,170],"</mml:math>":[26,171],"</inline-formula>":[27,172],"-variate":[28],"functions":[29],"that":[30,44,55,145,190],"have":[31],"a":[32,41,47,80,174],"weighted":[33,48,155],"tensor":[34,49],"product":[35,50],"form":[36],"and":[37,68,82,92,185],"are":[38],"endowed":[39],"with":[40],"Gaussian":[42],"measure":[43],"also":[45],"has":[46],"form.":[51],"Moreover,":[52],"we":[53,69],"assume":[54],"cost":[57,119,136],"evaluation":[60,118],"depends":[61],"on":[62,112],"number":[64,124],"active":[66,126],"variables":[67],"allow":[70],"it":[71],"to":[72,76,88,188],"be":[73,89],"from":[74],"linear":[75,149],"exponential.":[77,139],"provide":[79],"necessary":[81],"sufficient":[83],"condition":[84],"problem":[87,105,129],"polynomially":[90,107],"tractable":[91,108,132],"derive":[93],"exact":[95],"value":[96],"tractability":[99],"exponent.":[100],"In":[101],"particular,":[102],"is":[106,120,130,137],"under":[109],"modest":[110],"conditions":[111],"weights":[113],"even":[114,133],"if":[115,134],"exponential":[121],"variables.":[127],"The":[128],"weakly":[131],"this":[135,183],"doubly":[138],"These":[140],"results":[141,152],"hold":[142,153],"algorithms":[144,186],"can":[146],"use":[147,191],"unrestricted":[148],"information.":[150],"Similar":[151],"alttext=\"upper":[160],"L":[161],"2\">":[162],"<mml:msub>":[164],"<mml:mi>L</mml:mi>":[165],"<mml:mn>2</mml:mn>":[166],"</mml:msub>":[167],"encoding=\"application/x-tex\">L_2</mml:annotation>":[169],"approximation,":[173],"special":[175],"problems":[180],"considered":[181],"paper,":[184],"restricted":[187],"those":[189],"only":[192],"samplings.":[194]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
