{"id":"https://openalex.org/W4283387871","doi":"https://doi.org/10.1142/s0219691322500291","title":"EC-tractability of multivariate approximation in Hermite spaces for the standard information class","display_name":"EC-tractability of multivariate approximation in Hermite spaces for the standard information class","publication_year":2022,"publication_date":"2022-06-24","ids":{"openalex":"https://openalex.org/W4283387871","doi":"https://doi.org/10.1142/s0219691322500291"},"language":"en","primary_location":{"id":"doi:10.1142/s0219691322500291","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219691322500291","pdf_url":null,"source":{"id":"https://openalex.org/S56986848","display_name":"International Journal of Wavelets Multiresolution and Information Processing","issn_l":"0219-6913","issn":["0219-6913","1793-690X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Wavelets, Multiresolution and Information Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100436802","display_name":"Jie Zhang","orcid":"https://orcid.org/0000-0002-7954-8954"},"institutions":[{"id":"https://openalex.org/I44445938","display_name":"Shandong Jianzhu University","ror":"https://ror.org/01gbfax37","country_code":"CN","type":"education","lineage":["https://openalex.org/I44445938"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jie Zhang","raw_affiliation_strings":["College of Sciences, Shandong Jianzhu University, Jinan 250101, P. R. China"],"raw_orcid":"https://orcid.org/0000-0002-7954-8954","affiliations":[{"raw_affiliation_string":"College of Sciences, Shandong Jianzhu University, Jinan 250101, P. R. China","institution_ids":["https://openalex.org/I44445938"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100606521","display_name":"Yongping Liu","orcid":"https://orcid.org/0000-0003-3038-0270"},"institutions":[{"id":"https://openalex.org/I25254941","display_name":"Beijing Normal University","ror":"https://ror.org/022k4wk35","country_code":"CN","type":"education","lineage":["https://openalex.org/I25254941"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yongping Liu","raw_affiliation_strings":["Department of Mathematics, Beijing Normal University, Beijing 100875, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Beijing Normal University, Beijing 100875, P. R. China","institution_ids":["https://openalex.org/I25254941"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.09859155,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"20","issue":"06","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":0.9998999834060669,"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":0.9998999834060669,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9821000099182129,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hermite-polynomials","display_name":"Hermite polynomials","score":0.8330872058868408},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7264593243598938},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.6285966634750366},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.592620313167572},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.5596264004707336},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5328769087791443},{"id":"https://openalex.org/keywords/weight-function","display_name":"Weight function","score":0.49767473340034485},{"id":"https://openalex.org/keywords/univariate","display_name":"Univariate","score":0.492815762758255},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.4659111797809601},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4631269574165344},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.46216440200805664},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4548131227493286},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.43634268641471863},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4271220564842224},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.42137232422828674},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20898354053497314},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12777787446975708},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08970445394515991}],"concepts":[{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.8330872058868408},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7264593243598938},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.6285966634750366},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.592620313167572},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.5596264004707336},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5328769087791443},{"id":"https://openalex.org/C134466208","wikidata":"https://www.wikidata.org/wiki/Q1520657","display_name":"Weight function","level":2,"score":0.49767473340034485},{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.492815762758255},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.4659111797809601},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4631269574165344},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.46216440200805664},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4548131227493286},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.43634268641471863},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4271220564842224},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.42137232422828674},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20898354053497314},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12777787446975708},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08970445394515991},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0219691322500291","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219691322500291","pdf_url":null,"source":{"id":"https://openalex.org/S56986848","display_name":"International Journal of Wavelets Multiresolution and Information Processing","issn_l":"0219-6913","issn":["0219-6913","1793-690X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Wavelets, Multiresolution and Information Processing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1227297294","display_name":null,"funder_award_id":"11871006","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3953143477","display_name":null,"funder_award_id":"12101369","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W598051755","https://openalex.org/W1820164671","https://openalex.org/W1934971259","https://openalex.org/W1978653679","https://openalex.org/W1981743146","https://openalex.org/W2005840206","https://openalex.org/W2006791985","https://openalex.org/W2020865855","https://openalex.org/W2052335571","https://openalex.org/W2117631397","https://openalex.org/W2137224975","https://openalex.org/W2164084989","https://openalex.org/W2497677836","https://openalex.org/W2591645921","https://openalex.org/W2767507454","https://openalex.org/W2946175933","https://openalex.org/W2949870498","https://openalex.org/W2953976217","https://openalex.org/W2962718855","https://openalex.org/W2963374275","https://openalex.org/W2981844403","https://openalex.org/W3034271003","https://openalex.org/W3092263936","https://openalex.org/W3133617159","https://openalex.org/W3158843505","https://openalex.org/W3178042296","https://openalex.org/W4206333827","https://openalex.org/W4213059792"],"related_works":["https://openalex.org/W2885793850","https://openalex.org/W2005769942","https://openalex.org/W2916821264","https://openalex.org/W2108371780","https://openalex.org/W2971570150","https://openalex.org/W2111823044","https://openalex.org/W2789794956","https://openalex.org/W2034998431","https://openalex.org/W2991192738","https://openalex.org/W2055645274"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"study":[4],"exponential":[5],"tractability":[6,77,81],"of":[7,14,47,62,75,84,88],"multivariate":[8,51],"approximation":[9],"problem":[10],"for":[11,50,73],"Hermite":[12,35],"spaces":[13],"analytic":[15],"functions":[16,27],"over":[17],"[Formula:":[18,59],"see":[19,60],"text]":[20,61],"in":[21,82],"the":[22,31,57,89],"worst":[23],"case":[24],"setting.":[25],"The":[26,40],"are":[28,53],"characterized":[29],"by":[30],"property":[32],"that":[33],"their":[34],"coefficients":[36],"decay":[37],"exponentially":[38],"fast.":[39],"considered":[41],"algorithms":[42],"based":[43],"on":[44],"tensor":[45],"products":[46],"Gauss\u2013Hermite":[48],"rules":[49],"integration":[52],"constructive":[54],"and":[55,70,78],"use":[56],"class":[58],"only":[63],"function":[64],"evaluations.":[65],"We":[66],"give":[67],"matching":[68],"necessary":[69],"sufficient":[71],"conditions":[72],"notions":[74],"EC-quasi-polynomial":[76],"EC-uniform":[79],"weak":[80],"terms":[83],"two":[85],"weight":[86],"parameters":[87],"problem.":[90]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}