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

The algorithm of point-by-point approximation of multidimensional scalar function is discussed. The solution is searched as series of basic functions. Regularization of approximation is realized by inclusion of stabilizing functional in the Gaussian form. Regularization parameter is searched using Bayesian method. The proposed algorithm is very inexpensive from a computational point of view. In addition it has a unique analytical solution for regularization parameter in contrast to other Bayesian algorithms.