Bayesian regularization in the problem of point-by-point function approximation using an orthogonalized basis

An algorithm of approximation of a multidimensional point-by-point scalar function is considered. The solution is sought as a series in a set of basis functions. The approximation is regularized by the introduction of a stabilizing function in the Gaussian form; the parameter of regularization is sought by using the Bayesian approach. The proposed algorithm is inexpensive in terms of computations. Unlike other Bayesian models of approximation, it has a unique analytical solution for the regularization parameters.