Approximation of a Multidimensional Dependency Based on a Linear Expansion in a Dictionary of Parametric Functions (in English)
Belyaev M.G., Burnaev E.V.
Informatics and its Applications. 2013. V. 7, №. 3. P. 114-125.
We consider the problem of a multidimensional function approximation using a finite set of pairs "point"-"function value at this point". As a model for the function we use expansion in a dictionary containing non-linear parametric functions. Several sub-problems should be solve when constructing an approximation based on such model: extraction of a validation sample, initialization of parameters of the functions from the dictionary, tuning of these parameters. We propose efficient methods for solving these sub-problems. Efficiency of the proposed approach is demonstrated on some problems of engineering design.