approximation.

Polynomials, Orthogonal on Non-Uniform Grids

Authors: Nurmagomedov А. А.

Asymptotic properties of polynomials pˆn(t), orthogonal with weight ∆tj on any finite set of N points from segment [−1, 1] are investigated. Namely an asymptotic formula is proved in which asymptotic behaviour of these polynomials as n tends to infinity together with N is closely related to asymptotic behaviour of the Lasiandra polynomials. Furthermore are investigated the approximating properties of the sums by Fourier on these polynomials..

Simultaneous Approximation of Polynomial Functions and Its Derivatives by Feedforward Artificial Neural Networks with One Hidden Layer N. S.

Authors: Uzentsova N. S., Sidorov S. P.

 In this paper we propose the algorithm for finding weights of feedforward artificial neural networks with one hidden layer to approximate polynomial functions and its derivatives with a given error. We use the rational sigmoidal function as a transfer function.