{"id":"https://openalex.org/W2013738709","doi":"https://doi.org/10.1016/0893-6080(95)00124-7","title":"Approximating Functions by Neural Networks: A Constructive Solution in the Uniform Norm","display_name":"Approximating Functions by Neural Networks: A Constructive Solution in the Uniform Norm","publication_year":1996,"publication_date":"1996-08-01","ids":{"openalex":"https://openalex.org/W2013738709","doi":"https://doi.org/10.1016/0893-6080(95)00124-7","mag":"2013738709","pmid":"https://pubmed.ncbi.nlm.nih.gov/12662576"},"language":"en","primary_location":{"id":"doi:10.1016/0893-6080(95)00124-7","is_oa":true,"landing_page_url":"https://doi.org/10.1016/0893-6080(95)00124-7","pdf_url":null,"source":{"id":"https://openalex.org/S123019304","display_name":"Neural Networks","issn_l":"0893-6080","issn":["0893-6080","1879-2782"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Networks","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1016/0893-6080(95)00124-7","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085350260","display_name":"Mark Meltser","orcid":null},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Mark Meltser","raw_affiliation_strings":["Technion-Israel Institute of Technology,Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Technion-Israel Institute of Technology,Israel","institution_ids":["https://openalex.org/I174306211"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110288291","display_name":"Moshe Shoham","orcid":null},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Moshe Shoham","raw_affiliation_strings":["Technion-Israel Institute of Technology,Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Technion-Israel Institute of Technology,Israel","institution_ids":["https://openalex.org/I174306211"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080488049","display_name":"Larry M. Manevitz","orcid":null},"institutions":[{"id":"https://openalex.org/I90965887","display_name":"SUNY Polytechnic Institute","ror":"https://ror.org/000fxgx19","country_code":"US","type":"education","lineage":["https://openalex.org/I90965887"]},{"id":"https://openalex.org/I91203450","display_name":"University of Haifa","ror":"https://ror.org/02f009v59","country_code":"IL","type":"education","lineage":["https://openalex.org/I91203450"]}],"countries":["IL","US"],"is_corresponding":true,"raw_author_name":"Larry M. Manevitz","raw_affiliation_strings":["University of Haifa, Haifa, Israel","Polytechnic University,New York,USA","University of Haifa,Haifa,Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Haifa, Haifa, Israel","institution_ids":["https://openalex.org/I91203450"]},{"raw_affiliation_string":"Polytechnic University,New York,USA","institution_ids":["https://openalex.org/I90965887"]},{"raw_affiliation_string":"University of Haifa,Haifa,Israel","institution_ids":["https://openalex.org/I91203450"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5080488049"],"corresponding_institution_ids":["https://openalex.org/I90965887","https://openalex.org/I91203450"],"apc_list":{"value":3350,"currency":"USD","value_usd":3350},"apc_paid":{"value":3350,"currency":"USD","value_usd":3350},"fwci":1.1238,"has_fulltext":false,"cited_by_count":33,"citation_normalized_percentile":{"value":0.82862309,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"9","issue":"6","first_page":"965","last_page":"978"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9957000017166138,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9890000224113464,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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/constructive","display_name":"Constructive","score":0.839509129524231},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.7166814208030701},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6471913456916809},{"id":"https://openalex.org/keywords/uniform-norm","display_name":"Uniform norm","score":0.6064590811729431},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5842959880828857},{"id":"https://openalex.org/keywords/approximation-error","display_name":"Approximation error","score":0.504843533039093},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4463490843772888},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3907005786895752},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34255069494247437},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2091057300567627}],"concepts":[{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.839509129524231},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.7166814208030701},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6471913456916809},{"id":"https://openalex.org/C146324458","wikidata":"https://www.wikidata.org/wiki/Q1202673","display_name":"Uniform norm","level":2,"score":0.6064590811729431},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5842959880828857},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.504843533039093},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4463490843772888},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3907005786895752},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34255069494247437},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2091057300567627},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"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/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1016/0893-6080(95)00124-7","is_oa":true,"landing_page_url":"https://doi.org/10.1016/0893-6080(95)00124-7","pdf_url":null,"source":{"id":"https://openalex.org/S123019304","display_name":"Neural Networks","issn_l":"0893-6080","issn":["0893-6080","1879-2782"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Networks","raw_type":"journal-article"},{"id":"pmid:12662576","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/12662576","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural networks : the official journal of the International Neural Network Society","raw_type":null}],"best_oa_location":{"id":"doi:10.1016/0893-6080(95)00124-7","is_oa":true,"landing_page_url":"https://doi.org/10.1016/0893-6080(95)00124-7","pdf_url":null,"source":{"id":"https://openalex.org/S123019304","display_name":"Neural Networks","issn_l":"0893-6080","issn":["0893-6080","1879-2782"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Networks","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1573503290","https://openalex.org/W2026495637","https://openalex.org/W2027197837","https://openalex.org/W2027831574","https://openalex.org/W2103496339","https://openalex.org/W2137983211","https://openalex.org/W2766736793","https://openalex.org/W3121926921","https://openalex.org/W3125537303","https://openalex.org/W4300402905"],"related_works":["https://openalex.org/W2047048571","https://openalex.org/W2365662369","https://openalex.org/W2007276298","https://openalex.org/W1968390457","https://openalex.org/W2095404463","https://openalex.org/W1983792724","https://openalex.org/W4239376463","https://openalex.org/W2013738709","https://openalex.org/W2088884465","https://openalex.org/W1971359023"],"abstract_inverted_index":{"A":[0],"method":[1],"for":[2,60],"constructively":[3],"approximating":[4],"functions":[5],"in":[6,16,23,53,72,84],"the":[7,17,34,54,85],"uniform":[8,55],"(i.e.,":[9],"maximal":[10],"error)":[11],"norm":[12,56],"by":[13],"successive":[14],"changes":[15],"weights":[18],"and":[19,48,70],"number":[20,62],"of":[21,33,37,63],"neurons":[22],"a":[24,31,61],"neural":[25],"network":[26],"is":[27,30,57],"developed.":[28],"This":[29],"realization":[32],"approximation":[35,52],"results":[36],"Cybenko,":[38],"Hecht-Nielsen,":[39],"Hornik,":[40],"Stinchcombe,":[41],"White,":[42],"Gallant,":[43],"Funahashi,":[44],"Leshno":[45],"et":[46],"al.,":[47],"others.":[49],"The":[50],"constructive":[51],"more":[58,75],"appropriate":[59],"examples,":[64],"such":[65,78],"as":[66,79],"robotic":[67],"arm":[68],"motion,":[69],"stands":[71],"contrast":[73],"with":[74],"standard":[76],"methods,":[77],"back-propagation,":[80],"which":[81],"approximate":[82],"only":[83],"average":[86],"error":[87],"norm.":[88],"Copyright":[89],"1996":[90],"Elsevier":[91],"Science":[92],"Ltd":[93]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2026-07-27T08:26:11.824852","created_date":"2016-06-24T00:00:00"}