Approximation and Smoothing of Functions Based on Godunov Regularization

A new approach to function approximation is presented based on the ideas of S.K. Godunov on the regularization of ill-conditioned systems. The proposed method makes it possible to determine the values of functions at fine grid nodes based on data from a larger grid, while providing control over the smoothness of the resulting function. The estimates of convergence and smoothness are substantiated, and the results of computational experiments are presented illustrating the effectiveness of the proposed method.