{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,24]],"date-time":"2026-04-24T03:44:32Z","timestamp":1777002272526,"version":"3.51.4"},"reference-count":14,"publisher":"Elsevier BV","issue":"7","license":[{"start":{"date-parts":[[2000,9,1]],"date-time":"2000-09-01T00:00:00Z","timestamp":967766400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Networks"],"published-print":{"date-parts":[[2000,9]]},"DOI":"10.1016\/s0893-6080(00)00056-3","type":"journal-article","created":{"date-parts":[[2002,7,25]],"date-time":"2002-07-25T13:31:48Z","timestamp":1027603908000},"page":"695-697","source":"Crossref","is-referenced-by-count":17,"title":["Best approximation by Heaviside perceptron networks"],"prefix":"10.1016","volume":"13","author":[{"given":"P.","family":"Kainen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"V.","family":"K\u016frkov\u00e1","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A.","family":"Vogt","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/S0893-6080(00)00056-3_BIB1","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1007\/BF02551274","article-title":"Approximation by superpositions of a sigmoidal function","volume":"2","author":"Cybenko","year":"1989","journal-title":"Mathematics of Control, Signals and Systems"},{"key":"10.1016\/S0893-6080(00)00056-3_BIB2","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1007\/BF01171759","article-title":"Optimal nonlinear approximation","volume":"63","author":"DeVore","year":"1989","journal-title":"Manuscripta Mathematica"},{"key":"10.1016\/S0893-6080(00)00056-3_BIB3","series-title":"Foundations of modern analysis","author":"Friedman","year":"1982"},{"key":"10.1016\/S0893-6080(00)00056-3_BIB4","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1007\/BF00195855","article-title":"Networks and the best approximation property","volume":"63","author":"Girosi","year":"1990","journal-title":"Biological Cybernetics"},{"key":"10.1016\/S0893-6080(00)00056-3_BIB5","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1006\/jcss.1997.1506","article-title":"Approximation and learning of convex superpositions","volume":"55","author":"Gurvits","year":"1997","journal-title":"Journal of Computer and System Sciences"},{"key":"10.1016\/S0893-6080(00)00056-3_BIB6","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1016\/0893-6080(89)90020-8","article-title":"Multilayer feedforward networks are universal approximators","volume":"2","author":"Hornik","year":"1989","journal-title":"Neural Networks"},{"key":"10.1016\/S0893-6080(00)00056-3_BIB7","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/S0925-2312(99)00111-3","article-title":"Approximation by neural networks is not continuous","volume":"29","author":"Kainen","year":"1999","journal-title":"Neurocomputing"},{"key":"10.1016\/S0893-6080(00)00056-3_BIB8","unstructured":"Kainen, P.C., K\u016frkov\u00e1, V., Vogt, A. (1999). Best approximation by linear combinations of characteristic functions of half-spaces. Research report ICS-99-795."},{"key":"10.1016\/S0893-6080(00)00056-3_BIB9","first-page":"105","article-title":"Geometry and topology of continuous best and near best approximations","author":"Kainen","year":"2000","journal-title":"Journal of Approximation Theory"},{"key":"10.1016\/S0893-6080(00)00056-3_BIB10","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1016\/0893-6080(95)00027-W","article-title":"Approximation of functions by perceptron networks with bounded number of hidden units","volume":"8","author":"K\u016frkov\u00e1","year":"1995","journal-title":"Neural Networks"},{"key":"10.1016\/S0893-6080(00)00056-3_BIB11","doi-asserted-by":"crossref","first-page":"861","DOI":"10.1016\/S0893-6080(05)80131-5","article-title":"Multilayer feedforward networks with a nonpolynomial activation can approximate any function","volume":"6","author":"Leschno","year":"1993","journal-title":"Neural Networks"},{"key":"10.1016\/S0893-6080(00)00056-3_BIB12","series-title":"n-Width in approximation theory","author":"Pinkus","year":"1986"},{"key":"10.1016\/S0893-6080(00)00056-3_BIB13","series-title":"Best approximation in normed linear spaces by elements of linear subspaces","author":"Singer","year":"1970"},{"key":"10.1016\/S0893-6080(00)00056-3_BIB14","doi-asserted-by":"crossref","first-page":"776","DOI":"10.1007\/BF01146931","article-title":"Almost convex and Chebyshev sets","volume":"8","author":"Vlasov","year":"1970","journal-title":"Mathematical Notes of the Academy of Sciences, USSR"}],"container-title":["Neural Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0893608000000563?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0893608000000563?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,4,24]],"date-time":"2019-04-24T16:53:28Z","timestamp":1556124808000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0893608000000563"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,9]]},"references-count":14,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2000,9]]}},"alternative-id":["S0893608000000563"],"URL":"https:\/\/doi.org\/10.1016\/s0893-6080(00)00056-3","relation":{},"ISSN":["0893-6080"],"issn-type":[{"value":"0893-6080","type":"print"}],"subject":[],"published":{"date-parts":[[2000,9]]}}}