Approximation of Functions Defined in Tabular Form: Multicriteria Approach

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...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics 2023-05, Vol.63 (5), p.730-742
Main Authors: Nelyubin, A. P., Podinovski, V. V.
Format: Article
Language:English
Subjects:
Approximation
Computational Mathematics and Numerical Analysis
General Numerical Methods
Mathematical analysis
Mathematics
Mathematics and Statistics
Multiple criterion
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Summary: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.
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542523050147