{"id":"https://openalex.org/W2020990401","doi":"https://doi.org/10.1007/s10208-013-9149-9","title":"N-Widths and \u03b5-Dimensions for High-Dimensional Approximations","display_name":"N-Widths and \u03b5-Dimensions for High-Dimensional Approximations","publication_year":2013,"publication_date":"2013-04-03","ids":{"openalex":"https://openalex.org/W2020990401","doi":"https://doi.org/10.1007/s10208-013-9149-9","mag":"2020990401"},"language":"en","primary_location":{"id":"doi:10.1007/s10208-013-9149-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10208-013-9149-9","pdf_url":null,"source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","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/A5078668326","display_name":"\u00d0inh D\u0169ng","orcid":"https://orcid.org/0000-0003-2333-5623"},"institutions":[{"id":"https://openalex.org/I177233841","display_name":"Vietnam National University, Hanoi","ror":"https://ror.org/02jmfj006","country_code":"VN","type":"education","lineage":["https://openalex.org/I177233841"]}],"countries":["VN"],"is_corresponding":true,"raw_author_name":"Dinh D\u0169ng","raw_affiliation_strings":["Information Technology Institute, Vietnam National University, Hanoi, 144 Xuan Thuy, Hanoi, Vietnam","Vietnam National University, Hanoi"],"affiliations":[{"raw_affiliation_string":"Information Technology Institute, Vietnam National University, Hanoi, 144 Xuan Thuy, Hanoi, Vietnam","institution_ids":["https://openalex.org/I177233841"]},{"raw_affiliation_string":"Vietnam National University, Hanoi","institution_ids":["https://openalex.org/I177233841"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010819277","display_name":"Tino Ullrich","orcid":"https://orcid.org/0000-0002-0055-0542"},"institutions":[{"id":"https://openalex.org/I4391767997","display_name":"Hausdorff Center for Mathematics","ror":"https://ror.org/032n1tr36","country_code":null,"type":"facility","lineage":["https://openalex.org/I135140700","https://openalex.org/I4391767997"]},{"id":"https://openalex.org/I4210119692","display_name":"Numerical Method (China)","ror":"https://ror.org/02ns8zp42","country_code":"CN","type":"company","lineage":["https://openalex.org/I4210119692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tino Ullrich","raw_affiliation_strings":["Hausdorff-Center for Mathematics and Institute for Numerical Simulation, 53115, Bonn, Germany","Hausdorff-Center for Mathematics and Institute for Numerical Simulation"],"affiliations":[{"raw_affiliation_string":"Hausdorff-Center for Mathematics and Institute for Numerical Simulation, 53115, Bonn, Germany","institution_ids":["https://openalex.org/I4391767997"]},{"raw_affiliation_string":"Hausdorff-Center for Mathematics and Institute for Numerical Simulation","institution_ids":["https://openalex.org/I4210119692","https://openalex.org/I4391767997"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5078668326"],"corresponding_institution_ids":["https://openalex.org/I177233841"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":7.0777,"has_fulltext":false,"cited_by_count":41,"citation_normalized_percentile":{"value":0.9743071,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"13","issue":"6","first_page":"965","last_page":"1003"},"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.991100013256073,"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"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9828000068664551,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.871904730796814},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.6850781440734863},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5849230885505676},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.5534409284591675},{"id":"https://openalex.org/keywords/isotropy","display_name":"Isotropy","score":0.5260792970657349},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.5238107442855835},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.49408653378486633},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.4857495427131653},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4828794300556183},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.46464797854423523},{"id":"https://openalex.org/keywords/trigonometric-functions","display_name":"Trigonometric functions","score":0.44613462686538696},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.43953943252563477},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.4256936013698578},{"id":"https://openalex.org/keywords/trigonometry","display_name":"Trigonometry","score":0.42235782742500305},{"id":"https://openalex.org/keywords/infinity","display_name":"Infinity","score":0.42155811190605164},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4027247130870819},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12828177213668823},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.079445481300354},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07542651891708374}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.871904730796814},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.6850781440734863},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5849230885505676},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.5534409284591675},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.5260792970657349},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.5238107442855835},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.49408653378486633},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4857495427131653},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4828794300556183},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.46464797854423523},{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.44613462686538696},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.43953943252563477},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.4256936013698578},{"id":"https://openalex.org/C29001434","wikidata":"https://www.wikidata.org/wiki/Q8084","display_name":"Trigonometry","level":2,"score":0.42235782742500305},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.42155811190605164},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4027247130870819},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12828177213668823},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.079445481300354},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07542651891708374},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10208-013-9149-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10208-013-9149-9","pdf_url":null,"source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W5088572","https://openalex.org/W37878551","https://openalex.org/W108609485","https://openalex.org/W595326135","https://openalex.org/W602313805","https://openalex.org/W623509844","https://openalex.org/W1490039160","https://openalex.org/W1497839301","https://openalex.org/W1820164671","https://openalex.org/W1992187022","https://openalex.org/W1996674925","https://openalex.org/W2004485838","https://openalex.org/W2013576021","https://openalex.org/W2019377400","https://openalex.org/W2024729723","https://openalex.org/W2042108000","https://openalex.org/W2042587009","https://openalex.org/W2048708887","https://openalex.org/W2049119935","https://openalex.org/W2051553803","https://openalex.org/W2052806039","https://openalex.org/W2067393519","https://openalex.org/W2070656880","https://openalex.org/W2075646404","https://openalex.org/W2093680504","https://openalex.org/W2110888545","https://openalex.org/W2114888017","https://openalex.org/W2116514123","https://openalex.org/W2130500373","https://openalex.org/W2135329423","https://openalex.org/W2135512293","https://openalex.org/W2136128169","https://openalex.org/W2151043893","https://openalex.org/W2164158544","https://openalex.org/W2243133321","https://openalex.org/W2316762840","https://openalex.org/W2329522476","https://openalex.org/W2341171179","https://openalex.org/W2403013574","https://openalex.org/W2497677836","https://openalex.org/W2522450843","https://openalex.org/W2798679239","https://openalex.org/W3109334054","https://openalex.org/W3119524009","https://openalex.org/W4255975175","https://openalex.org/W4299521717","https://openalex.org/W6602007479"],"related_works":["https://openalex.org/W2972113003","https://openalex.org/W4288323582","https://openalex.org/W2951617381","https://openalex.org/W2006551014","https://openalex.org/W2987292777","https://openalex.org/W634571496","https://openalex.org/W579400037","https://openalex.org/W2951578208","https://openalex.org/W1570037808","https://openalex.org/W4298173607"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-26T15:22:09.906841","created_date":"2025-10-10T00:00:00"}
