{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T21:54:36Z","timestamp":1725486876153},"publisher-location":"Berlin, Heidelberg","reference-count":22,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540715900"},{"type":"electronic","value":"9783540716297"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"DOI":"10.1007\/978-3-540-71629-7_2","type":"book-chapter","created":{"date-parts":[[2007,7,3]],"date-time":"2007-07-03T02:33:31Z","timestamp":1183430011000},"page":"11-18","source":"Crossref","is-referenced-by-count":5,"title":["Estimates of Approximation Rates by Gaussian Radial-Basis Functions"],"prefix":"10.1007","author":[{"given":"Paul C.","family":"Kainen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"V\u011bra","family":"K\u016frkov\u00e1","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marcello","family":"Sanguineti","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"2_CR1","volume-title":"Sobolev Spaces","author":"R.A. Adams","year":"2003","unstructured":"Adams, R.A., Fournier, J.J.F.: Sobolev Spaces. Academic Press, Amsterdam (2003)"},{"key":"2_CR2","first-page":"69","volume-title":"Proc. 7th Yale Workshop on Adaptive and Learning Systems","author":"A.R. Barron","year":"1992","unstructured":"Barron, A.R.: Neural net approximation. In: Narendra, K. (ed.) Proc. 7th Yale Workshop on Adaptive and Learning Systems, pp. 69\u201372. Yale University Press, New Haven (1992)"},{"key":"2_CR3","doi-asserted-by":"publisher","first-page":"930","DOI":"10.1109\/18.256500","volume":"39","author":"A.R. Barron","year":"1993","unstructured":"Barron, A.R.: Universal approximation bounds for superpositions of a sigmoidal function. IEEE Transactions on Information Theory\u00a039, 930\u2013945 (1993)","journal-title":"IEEE Transactions on Information Theory"},{"key":"2_CR4","volume-title":"Special Functions of Applied Mathematics","author":"B.C. Carlson","year":"1977","unstructured":"Carlson, B.C.: Special Functions of Applied Mathematics. Academic Press, New York (1977)"},{"key":"2_CR5","unstructured":"Girosi, F.: Approximation error bounds that use VC-bounds. In: Proceedings of the International Conference on Neural Networks, Paris, pp. 295\u2013302 (1995)"},{"key":"2_CR6","first-page":"97","volume-title":"Artificial Neural Networks for Speech and Vision","author":"F. Girosi","year":"1993","unstructured":"Girosi, F., Anzellotti, G.: Rates of convergence for radial basis functions and neural networks. In: Mammone, R.J. (ed.) Artificial Neural Networks for Speech and Vision, pp. 97\u2013113. Chapman & Hall, London (1993)"},{"key":"2_CR7","doi-asserted-by":"publisher","first-page":"210","DOI":"10.1162\/neco.1990.2.2.210","volume":"2","author":"E.J. Hartman","year":"1990","unstructured":"Hartman, E.J., Keeler, J.D., Kowalski, J.M.: Layered neural networks with Gaussian hidden units as universal approximations. Neural Computation\u00a02, 210\u2013215 (1990)","journal-title":"Neural Computation"},{"key":"2_CR8","doi-asserted-by":"publisher","first-page":"608","DOI":"10.1214\/aos\/1176348546","volume":"20","author":"L.K. Jones","year":"1992","unstructured":"Jones, L.K.: A simple lemma on greedy approximation in Hilbert space and convergence rates for projection pursuit regression and neural network training. Annals of Statistics\u00a020, 608\u2013613 (1992)","journal-title":"Annals of Statistics"},{"key":"2_CR9","unstructured":"Kainen, P.C., Kurkov\u00e1, V., Sanguineti, M.: Rates of approximation of smooth functions by Gaussian radial-basis- function networks. Research report ICS\u2013976 (2006), \n                    \n                      http:\/\/www.cs.cas.cz\/research\/publications.shtml"},{"key":"2_CR10","first-page":"67","volume":"3","author":"M.A. Kon","year":"2005","unstructured":"Kon, M.A., Raphael, L.A., Williams, D.A.: Extending Girosi\u2019s approximation estimates for functions in Sobolev spaces via statistical learning theory. J. of Analysis and Applications\u00a03, 67\u201390 (2005)","journal-title":"J. of Analysis and Applications"},{"key":"2_CR11","unstructured":"Kon, M.A., Raphael, L.A.: Approximating functions in reproducing kernel Hilbert spaces via statistical learning theory. Preprint (2005)"},{"key":"2_CR12","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1007\/978-1-4612-1996-5_16","volume-title":"Computer\u2013Intensive Methods in Control and Signal Processing: Curse of Dimensionality","author":"V. Kurkov\u00e1","year":"1997","unstructured":"Kurkov\u00e1, V.: Dimension\u2013independent rates of approximation by neural networks. In: Warwick, K., K\u00e1rn\u00fd, M. (eds.) Computer\u2013Intensive Methods in Control and Signal Processing: Curse of Dimensionality, pp. 261\u2013270. Birkh\u00e4user, Basel (1997)"},{"key":"2_CR13","first-page":"69","volume-title":"Advances in Learning Theory: Methods, Models and Applications","author":"V. Kurkov\u00e1","year":"2003","unstructured":"Kurkov\u00e1, V.: High-dimensional approximation and optimization by neural networks. In: Suykens, J., et al. (eds.) Advances in Learning Theory: Methods, Models and Applications, pp. 69\u201388. IOS Press, Amsterdam (2003)"},{"key":"2_CR14","doi-asserted-by":"publisher","first-page":"1061","DOI":"10.1016\/S0893-6080(97)00028-2","volume":"10","author":"V. Kurkov\u00e1","year":"1997","unstructured":"Kurkov\u00e1, V., Kainen, P.C., Kreinovich, V.: Estimates of the number of hidden units and variation with respect to half-spaces. Neural Networks\u00a010, 1061\u20131068 (1997)","journal-title":"Neural Networks"},{"key":"2_CR15","volume-title":"The Theory of Fractional Powers of Operators","author":"C. Mart\u00ednez","year":"2001","unstructured":"Mart\u00ednez, C., Sanz, M.: The Theory of Fractional Powers of Operators. Elsevier, Amsterdam (2001)"},{"key":"2_CR16","unstructured":"Mhaskar, H.N.: Versatile Gaussian networks. In: Proc. IEEE Workshop of Nonlinear Image Processing, pp. 70\u201373 (1995)"},{"key":"2_CR17","doi-asserted-by":"publisher","first-page":"350","DOI":"10.1016\/0196-8858(92)90016-P","volume":"13","author":"H.N. Mhaskar","year":"1992","unstructured":"Mhaskar, H.N., Micchelli, C.A.: Approximation by superposition of a sigmoidal function and radial basis functions. Advances in Applied Mathematics\u00a013, 350\u2013373 (1992)","journal-title":"Advances in Applied Mathematics"},{"key":"2_CR18","doi-asserted-by":"publisher","first-page":"246","DOI":"10.1162\/neco.1991.3.2.246","volume":"3","author":"J. Park","year":"1991","unstructured":"Park, J., Sandberg, I.W.: Universal approximation using radial\u2013basis\u2013function networks. Neural Computation\u00a03, 246\u2013257 (1991)","journal-title":"Neural Computation"},{"key":"2_CR19","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1162\/neco.1993.5.2.305","volume":"5","author":"J. Park","year":"1993","unstructured":"Park, J., Sandberg, I.: Approximation and radial basis function networks. Neural Computation\u00a05, 305\u2013316 (1993)","journal-title":"Neural Computation"},{"key":"2_CR20","unstructured":"Pisier, G.: Remarques sur un resultat non publi\u00e9 de B. Maurey. In: Seminaire d\u2019Analyse Fonctionelle, vol. I(12), pp. 1980\u20131981, \u00c9cole Polytechnique, Centre de Math\u00e9matiques, Palaiseau"},{"key":"2_CR21","volume-title":"Singular Integrals and Differentiability Properties of Functions","author":"E.M. Stein","year":"1970","unstructured":"Stein, E.M.: Singular Integrals and Differentiability Properties of Functions. Princeton University Press, Princeton (1970)"},{"key":"2_CR22","doi-asserted-by":"crossref","DOI":"10.1142\/5314","volume-title":"A Guide to Distribution Theory and Fourier Transforms","author":"R. Strichartz","year":"2003","unstructured":"Strichartz, R.: A Guide to Distribution Theory and Fourier Transforms. World Scientific, Hackensack (2003)"}],"container-title":["Lecture Notes in Computer Science","Adaptive and Natural Computing Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-71629-7_2.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,19]],"date-time":"2020-11-19T05:23:52Z","timestamp":1605763432000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-71629-7_2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[null]]},"ISBN":["9783540715900","9783540716297"],"references-count":22,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-71629-7_2","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[]}}