Approximation and smoothing of a function based on Godunov regularization

A new approach to function approximation is presented, based on S.K. Godunov’s ideas on the regularization of ill-conditioned systems. The proposed method allows for determining function values at nodes of a finer grid from data on a coarser grid while ensuring control over the smoothness of the resulting function. Convergence and smoothness estimates are substantiated, and results from computational experiments illustrate the effectiveness of the proposed method.