We prove that neural networks with a single hidden layer are capable of providing an optimal order of approximation for functions assumed to possess a given number of derivatives, if the activationâ€¦ (More)

Geodetic and meteorological data, collected via satellites for example, are genuinely scattered, and not confined to any special set of points. Even so, known quadrature formulas used in numericallyâ€¦ (More)

We prove that an artificial neural network with multiple hidden layers and a kthorder sigmoidal response function can be used to approximate any continuous function on any compact subset of aâ€¦ (More)

A zonal function (ZF) network is a function of the form x 7â†’ âˆ‘n k=1 ckÏ†(x Â· yk), where x and the ykâ€™s are on the on the unit sphere in q+1 dimensional Euclidean space, and where the ykâ€™s areâ€¦ (More)

Let q â‰¥ 1 be an integer, Sq be the unit sphere embedded in the Euclidean space Rq+1. A Zonal Function (ZF) network with an activation function Ï† : [âˆ’1, 1] â†’ R and n neurons is a function on Sq of theâ€¦ (More)

We obtain a characterization of local Besov spaces of functions on [âˆ’1, 1] in terms of algebraic polynomial operators. These operators are constructed using the coefficients in the orthogonalâ€¦ (More)

Let s > or = 1 be an integer. A Gaussian network is a function on Rs of the form [Formula: see text]. The minimal separation among the centers, defined by (1/2) min(1 < or = j not = k < or = N)â€¦ (More)

Let s/> 1 be an integer and W be the class of all functions having integrable partial derivatives on [0, 1] s. We are interested in the minimum number of neurons in a neural network with a singleâ€¦ (More)