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Approximation of Functions Defined in Tabular Form: Multicriteria Approach
Computational Mathematics and Mathematical Physics. 2023. Vol. 63. No. 5. P. 730–742.
A. P. Nelyubin, V. V. Podinovski
A new approach to estimating approximation parameters is developed. In this approach, the
distance of the approximating function from a given finite set of points is estimated by a vector criterion
the components of which are the absolute values of residuals at all points. Using this criterion, the
remoteness preference relation is defined, and the nondominated function with respect to this relation
is considered to be the best approximating function. Approximation for several preference relations is
studied, including the Pareto relation and the relation generated by the information about the equal
importance of the criteria. Computational issues are considered and the relationship between the
introduced approximating functions and the classical ones (obtained by the methods of least squares,
least modulus, and the least maximum absolute value of deviation) are considered.
Keywords: criteria importance theoryтеория важности критериеврегрессионный анализаппроксимация функцийregression analysisapproximation of functionsмногокритериальный анализmulticriteria analysis,
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