Multivariate Hermite interpolation by algebraic polynomials: a survey
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 vol. II: interpolation and extrapolation
Properties of the Hermite Activation Functions in a Neural Approximation Scheme
ICANNGA '07 Proceedings of the 8th international conference on Adaptive and Natural Computing Algorithms, Part II
Approximation of functions by multivariable hermite basis: a hybrid method
ICANNGA'11 Proceedings of the 10th international conference on Adaptive and natural computing algorithms - Volume Part I
IEEE Transactions on Neural Networks
Objective functions for training new hidden units in constructive neural networks
IEEE Transactions on Neural Networks
Constructive feedforward neural networks using Hermite polynomial activation functions
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
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A method of multivariable (multivariate) Hermite function based approximation is presented and discussed. The multivariable basis is constructed as a product of one-variable Hermite functions with adjustable scaling parameters. Thanks basis orthonormality, the approximated function expansion coefficients are calculated by using explicit, non-search formulae. The scaling parameters are determined via a search algorithm. Initially, an excessive number of functions in the basis is calculated, then a simple pruning method is applied. Only those are taken which contribute the most to error decrease, down to a desired level. The method ensures a very good generalization property. This claim is supported by both theoretical considerations and working examples.