Approximation of Functions Defined in Tabular Form. II

This paper continues the development of a new approach to estimating approximation parameters in which the distance of the approximating function from a given finite set of points is estimated by a vector criterion whose components are the moduli of the residuals at all points. Using this vector criterion, a preference relation in terms of distance is defined, and the approximating function that is not dominated by such a relation is considered the best. Unlike the first paper of the authors (Computational Mathematics and Mathematical Physics, 2022), which is devoted to parametric methods, this paper proposes nonparametric methods for several preference relations, including the Pareto relation and the relation generated by information about the equal importance of criteria. Computational issues are considered and the relationships between the introduced approximating functions and classical ones are investigated. Numerical examples are discussed.