{"id":"https://openalex.org/W4393090391","doi":"https://doi.org/10.1137/22m1525193","title":"On the Approximability and Curse of Dimensionality of Certain Classes of High-Dimensional Functions","display_name":"On the Approximability and Curse of Dimensionality of Certain Classes of High-Dimensional Functions","publication_year":2024,"publication_date":"2024-03-22","ids":{"openalex":"https://openalex.org/W4393090391","doi":"https://doi.org/10.1137/22m1525193"},"language":"en","primary_location":{"id":"doi:10.1137/22m1525193","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1525193","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":["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/A5110275232","display_name":"Christian Rieger","orcid":null},"institutions":[{"id":"https://openalex.org/I161103922","display_name":"Philipps University of Marburg","ror":"https://ror.org/01rdrb571","country_code":"DE","type":"education","lineage":["https://openalex.org/I161103922"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Christian Rieger","raw_affiliation_strings":["FB Mathematik und Informatik, Philipps-Universit\u00e4t Marburg, 35032 Marburg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"FB Mathematik und Informatik, Philipps-Universit\u00e4t Marburg, 35032 Marburg, Germany","institution_ids":["https://openalex.org/I161103922"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066096555","display_name":"Holger Wendland","orcid":"https://orcid.org/0000-0002-9614-5321"},"institutions":[{"id":"https://openalex.org/I54009628","display_name":"University of Bayreuth","ror":"https://ror.org/0234wmv40","country_code":"DE","type":"education","lineage":["https://openalex.org/I54009628"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Holger Wendland","raw_affiliation_strings":["Department of Mathematics, University of Bayreuth, 95440 Bayreuth, Germany"],"raw_orcid":"https://orcid.org/0000-0002-9614-5321","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Bayreuth, 95440 Bayreuth, Germany","institution_ids":["https://openalex.org/I54009628"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5110275232"],"corresponding_institution_ids":["https://openalex.org/I161103922"],"apc_list":null,"apc_paid":null,"fwci":5.6459,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.9649307,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"62","issue":"2","first_page":"842","last_page":"871"},"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9528999924659729,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9524000287055969,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8170174360275269},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.8121512532234192},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3867284059524536},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.321771502494812},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.27203547954559326},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08466634154319763}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8170174360275269},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.8121512532234192},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3867284059524536},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.321771502494812},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.27203547954559326},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08466634154319763}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/22m1525193","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1525193","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"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.5600000023841858}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W39759813","https://openalex.org/W50417968","https://openalex.org/W76303595","https://openalex.org/W79383899","https://openalex.org/W1820164671","https://openalex.org/W1867316708","https://openalex.org/W1986280275","https://openalex.org/W2027338456","https://openalex.org/W2044594221","https://openalex.org/W2070330278","https://openalex.org/W2100179204","https://openalex.org/W2142863015","https://openalex.org/W2150612352","https://openalex.org/W2169658509","https://openalex.org/W2482768955","https://openalex.org/W2497677836","https://openalex.org/W2523698989","https://openalex.org/W2537590198","https://openalex.org/W2913715598","https://openalex.org/W3008609509","https://openalex.org/W3036627574","https://openalex.org/W3087815761","https://openalex.org/W3178042296","https://openalex.org/W3196290810","https://openalex.org/W3199698735","https://openalex.org/W3216135771","https://openalex.org/W4237171445","https://openalex.org/W4255975175","https://openalex.org/W4300580367"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W4296209631","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793","https://openalex.org/W4238204885"],"abstract_inverted_index":{".In":[0],"this":[1],"paper,":[2],"we":[3],"study":[4],"the":[5,15,50,65],"approximability":[6],"of":[7,17,35,52,67,72],"high-dimensional":[8,22],"functions":[9,60],"that":[10,58],"appear,":[11],"for":[12,43],"example,":[13],"in":[14],"context":[16],"many":[18],"body":[19],"expansions":[20],"and":[21,56],"model":[23,70],"representation.":[24],"Such":[25],"functions,":[26,45],"though":[27],"high-dimensional,":[28],"can":[29],"be":[30],"represented":[31],"as":[32],"finite":[33],"sums":[34],"lower-dimensional":[36],"functions.":[37],"We":[38],"will":[39],"derive":[40],"sampling":[41,54],"inequalities":[42],"such":[44,59],"give":[46],"explicit":[47],"advice":[48],"on":[49],"location":[51],"good":[53],"points,":[55],"show":[57],"do":[61],"not":[62],"suffer":[63],"from":[64],"curse":[66],"dimensionality.Keywordshigh-dimensional":[68],"approximationhigh-dimensional":[69],"representationcurse":[71],"dimensionalitymixed":[73],"regularity":[74],"Sobolev":[75],"spacessampling":[76],"inequalitiesMSC":[77],"codes65D0541A2541A63":[78]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
