{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T10:45:31Z","timestamp":1760265931089},"reference-count":25,"publisher":"Elsevier BV","issue":"1","license":[{"start":{"date-parts":[[1998,9,1]],"date-time":"1998-09-01T00:00:00Z","timestamp":904608000000},"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":["Applied Mathematics and Computation"],"published-print":{"date-parts":[[1998,9]]},"DOI":"10.1016\/s0096-3003(97)10089-3","type":"journal-article","created":{"date-parts":[[2003,4,30]],"date-time":"2003-04-30T21:18:06Z","timestamp":1051737486000},"page":"75-89","source":"Crossref","is-referenced-by-count":18,"title":["On simultaneous approximations by radial basis function neural networks"],"prefix":"10.1016","volume":"95","author":[{"given":"Xin","family":"Li","sequence":"first","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/S0096-3003(97)10089-3_BIB1","doi-asserted-by":"crossref","first-page":"930","DOI":"10.1109\/18.256500","article-title":"Universal approximation bounds for superpositions of a sigmoidal function","volume":"39","author":"Barron","year":"1993","journal-title":"IEEE Trans. Inf. Theory"},{"key":"10.1016\/S0096-3003(97)10089-3_BIB2","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/S0893-6080(05)80020-6","article-title":"Approximation of a function and its derivatives with a neural network","volume":"5","author":"Cardaliaguet","year":"1992","journal-title":"Neural Networks"},{"key":"10.1016\/S0096-3003(97)10089-3_BIB3","doi-asserted-by":"crossref","first-page":"904","DOI":"10.1109\/72.392252","article-title":"Approximation capability to functions of several variables, nonlinear functionals, and operators by radial basis function neural networks","volume":"6","author":"Chen","year":"1995","journal-title":"IEEE Trans. Neural Networks"},{"key":"10.1016\/S0096-3003(97)10089-3_BIB4","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1090\/S0025-5718-1994-1240656-2","article-title":"Neural networks for localized approximation","volume":"6","author":"Chui","year":"1994","journal-title":"Math. Comput."},{"key":"10.1016\/S0096-3003(97)10089-3_BIB5","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1007\/BF02124745","article-title":"Limitations on the approximation capabilities of neural networks with one hidden layer","volume":"5","author":"Chui","year":"1996","journal-title":"Adv. Comput. Math."},{"key":"10.1016\/S0096-3003(97)10089-3_BIB6","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":"Math. Control Signals Syst."},{"key":"10.1016\/S0096-3003(97)10089-3_BIB7","doi-asserted-by":"crossref","first-page":"332","DOI":"10.1109\/72.363469","article-title":"Accuracy analysis for wavelet approximations","volume":"6","author":"Delyon","year":"1995","journal-title":"IEEE Trans. Neural Networks"},{"key":"10.1016\/S0096-3003(97)10089-3_BIB8","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/S0893-6080(05)80011-5","article-title":"On learning the derivatives of an unknown mapping with multilayer feedforward networks","volume":"5","author":"Gallant","year":"1992","journal-title":"Neural Networks"},{"key":"10.1016\/S0096-3003(97)10089-3_BIB9","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1162\/neco.1990.2.2.210","article-title":"Layered neural networks with Gaussian hidden units as universal approximators","volume":"2","author":"Hartman","year":"1990","journal-title":"Neural Comput."},{"key":"10.1016\/S0096-3003(97)10089-3_BIB10","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\/S0096-3003(97)10089-3_BIB11","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1016\/0893-6080(90)90005-6","article-title":"Universal approximation of an unknown mapping and its derivatives using feedforward networks","volume":"3","author":"Hornik","year":"1990","journal-title":"Neural Networks"},{"key":"10.1016\/S0096-3003(97)10089-3_BIB12","doi-asserted-by":"crossref","first-page":"608","DOI":"10.1214\/aos\/1176348546","article-title":"A simple lemma on greedy approximation in Hilbert space and convergence rates for projection pursuit regression and neural network training","volume":"20","author":"Jones","year":"1992","journal-title":"Ann. Statist."},{"key":"10.1016\/S0096-3003(97)10089-3_BIB13","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/0893-6080(91)90005-P","article-title":"A gaussian potential function network with hierarchically self-organizing learning","volume":"4","author":"Lee","year":"1991","journal-title":"Neural Networks"},{"key":"10.1016\/S0096-3003(97)10089-3_BIB14","doi-asserted-by":"crossref","first-page":"861","DOI":"10.1016\/S0893-6080(05)80131-5","article-title":"Multilayer feedforward networks with a nonpolynomial activation function can approximate any function","volume":"6","author":"Leshno","year":"1993","journal-title":"Neural Networks"},{"key":"10.1016\/S0096-3003(97)10089-3_BIB15","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1016\/0925-2312(95)00070-4","article-title":"Simultaneous approximations of multivariate functions and their derivatives by neural networks with one hidden layer","volume":"12","author":"Li","year":"1996","journal-title":"Neurocomputing"},{"key":"10.1016\/S0096-3003(97)10089-3_BIB16","doi-asserted-by":"crossref","first-page":"350","DOI":"10.1016\/0196-8858(92)90016-P","article-title":"Approximation by superposition of a sigmoidal function","volume":"13","author":"Mhaskar","year":"1992","journal-title":"Adv. Appl. Math."},{"key":"10.1016\/S0096-3003(97)10089-3_BIB17","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/0021-9045(91)90087-Q","article-title":"Norms of inverses and condition numbers for matrices associated with scattered data","volume":"64","author":"Narcowich","year":"1991","journal-title":"J. Approxim. Theory"},{"key":"10.1016\/S0096-3003(97)10089-3_BIB18","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1162\/neco.1991.3.2.246","article-title":"Universal approximation using radial basis function networks","volume":"3","author":"Park","year":"1991","journal-title":"Neural Comput."},{"key":"10.1016\/S0096-3003(97)10089-3_BIB19","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1162\/neco.1993.5.2.305","article-title":"Approximation and radial basis function networks","volume":"5","author":"Park","year":"1993","journal-title":"Neural Comput."},{"key":"10.1016\/S0096-3003(97)10089-3_BIB20","article-title":"Remarques sur un resultat non publie de B. Maurey","volume":"vol. 1\u201312","author":"Pisier","year":"1981"},{"key":"10.1016\/S0096-3003(97)10089-3_BIB21","article-title":"A theory of networks for approximation and learning","author":"Poggio","year":"1989"},{"key":"10.1016\/S0096-3003(97)10089-3_BIB22","first-page":"1481","article-title":"Networks for approximation and learning","volume":"78","author":"Poggio","year":"1990"},{"key":"10.1016\/S0096-3003(97)10089-3_BIB23","series-title":"Functional Analysis","author":"Rudin","year":"1973"},{"key":"10.1016\/S0096-3003(97)10089-3_BIB24","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1109\/72.363455","article-title":"Existence and uniqueness results for neural network approximations","volume":"6","author":"Williamson","year":"1995","journal-title":"IEEE Trans. Neural Networks"},{"key":"10.1016\/S0096-3003(97)10089-3_BIB25","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1007\/BF00126430","article-title":"A mathematical analysis of the motion coherence theory","volume":"3","author":"Yuille","year":"1989","journal-title":"Int. J. Computer Vision"}],"container-title":["Applied Mathematics and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0096300397100893?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0096300397100893?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,5,2]],"date-time":"2019-05-02T00:25:52Z","timestamp":1556756752000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0096300397100893"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,9]]},"references-count":25,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1998,9]]}},"alternative-id":["S0096300397100893"],"URL":"https:\/\/doi.org\/10.1016\/s0096-3003(97)10089-3","relation":{},"ISSN":["0096-3003"],"issn-type":[{"value":"0096-3003","type":"print"}],"subject":[],"published":{"date-parts":[[1998,9]]}}}