thesIt » universal approximation property http://lakm.us/thesit computer science research log in semi microbloging style Tue, 24 Aug 2010 21:34:55 +0000 http://wordpress.org/?v=2.9 en hourly 1 Approximation Capabilities of Neural Net … http://lakm.us/thesit/296/approximation-capabilities-of-neural-net/ http://lakm.us/thesit/296/approximation-capabilities-of-neural-net/#comments Wed, 11 Aug 2010 19:27:51 +0000 Arif http://xp-racy.lan/s2/?p=296 Approximation Capabilities of Neural Networks. C. Enăchescu, Journal of Numerical Analysis, Industrial and Applied Mathematics (JNAIAM), vol. 3, no. 3-4, 2008, pp. 221-230

From the learning point of view, the approximation of a function is equivalent with the learning problem of a neural network. In this paper we want to show the capabilities of a neural network to approximate arbitrary continuous functions. We have made some experiments in order to confirm the theoretical results.

c48613aed54c29e0f60ca35833aebf70.pdf

f : X \subseteq R^{n} \to R^{m} is a continuous function

Neural Network and Best Approximation Theory

Given f \in F and A \subseteq F we call the distance of f from A as d(f,A)=inf\left \| f-a \right \|, a\in A

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