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.

approximation, function smoothing, regularization of ill-conditioned systems of linear equations