Abstract:
The article continues the development of a new approach to evaluate approximation parameters, in which the distance of the approximating function from the given finite set of points is estimated by a vector criterion, its components are the modules of residuals at all points. The vector criterion is used to define the distance preference ratio, and the best approximation function is considered to be nondominant with respect to this ratio. Compared to the first article of the authors (“Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki”, 2022), which is devoted to parametric methods, the present article offers nonparametric methods for several preference relations, including the Pareto relation and the relation generated by the information about the equality of criteria. Computational problems are considered and the relations between the introduced approximating functions and classical ones are investigated. Calculated examples are provided.
