Neural network interpolation operators of multivariate functions

In this paper, we introduce a type of multivariate neural network interpolation operators Fn,sigma(f) activated by some newly defined sigmoidal functions, and give both the direct and the converse results of the approximation by Fn,sigma(f) for multivariate continuous functions. We also introduce a Kantorovich type variant of Fn,sigma(f), and establish both the direct theorem and the converse theorem of approximation by the Kantorovich type operators in Lp spaces with 1 < p < oo. Finally, we give some numerical examples to demonstrate the validity of the obtained results, and apply our operators to the image super-resolution reconstruction.(c) 2023 Elsevier B.V. All rights reserved.