Approximate interpolation by neural networks with the inverse multiquadric functions

Authors:
Xuli Han
Affiliations:
School of Mathematical Sciences and Computing Technology, Central South University, Changsha, China
Venue:
ISICA'07 Proceedings of the 2nd international conference on Advances in computation and intelligence
Year:
2007

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Abstract

For approximate interpolation, a type of single-hidden layer feedforward neural networks with the inverse multiquadric activation function is presented in this paper. We give a new and quantitative proof of the fact that a single layer neural networks with n+1 hidden neurons can learn n + 1 distinct samples with zero error. Based on this result, approximate interpolants are given. They can approximate interpolate, with arbitrary precision, any set of distinct data in one or several dimensions. They can uniformly approximate any C1 continuous function of one variable.