Higher Order Convergence of a Multivariate Neural Network Interpolation Operator for Irregular Grid

This paper provides interpolation and approximation techniques for continuous functions defined on an irregular grid within a box-domain of Rd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}<^>{d}$$\end{document}, using a new family of neural networks interpolation operators based on Lagrange polynomials. The approximation error is estimated by using higher order moduli of smoothness of the functions considered.