Affiliation:
1. Department of Mathematics and Computer Sciences 1, Via Vanvitelli 06123-I Perugia Italy
Abstract
Abstract
The theory of multivariate neural network operators in a Kantorovich type version is here introduced and studied. The main results concerns the approximation of multivariate data, with respect to the uniform and Lp
norms, for continuous and Lp
functions, respectively. The above family of operators, are based upon kernels generated by sigmoidal functions. Multivariate approximation by constructive neural network algorithms are useful for applications to neurocomputing processes involving high dimensional data. At the end of the paper, several examples of sigmoidal functions for which the above theory holds have been presented.
Reference54 articles.
1. Amari, S.—Cichocki, A.—Yang, H. H.: A new learning algorithm for blind signal separation, Advances in neural information processing systems (1996), 757–763.
2. Anastassiou, G. A.: Intelligent Systems: Approximation by Artificial Neural Networks. In: Intelligent Systems Reference Library 19, Springer-Verlag, Berlin, 2011.
3. Anastassiou, G. A.—Coroianu, L.—Gal, S. G.: Approximation by a nonlinear Cardaliaguet-Euvrard neural network operator of max-product kind, J. Comp. Anal. Appl. 12 (2010), 396–406.
4. Angeloni, L.—Vinti, G.: Approximation in variation by homothetic operators in multidimensional setting, Differential Integral Equations 26 (2013), 655–674.
5. Angeloni, L.—Vinti, G.: Convergence and rate of approximation in BVφ(R+N)$BV_\varphi(\mathbb R_+^N)$ for a class of Mellin integral operators, Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni 25 (2014), 217–232.
Cited by
16 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献