EPJ Web Conf.
Volume 173, 2018Mathematical Modeling and Computational Physics 2017 (MMCP 2017)
|Number of page(s)||4|
|Section||Numerical Modeling and Methods|
|Published online||14 February 2018|
Extrapolation of Functions of Many Variables by Means of Metric Analysis
1 National Research Nuclear University “MEPhI”, Moscow, Russia
2 Joint Institute for Nuclear Research (JINR), Dubna, Moscow region, Russia
3 Peoples’ Frendship University of Russia (PFUR University), Moscow, Russia
4 University of Miami, USA
Published online: 14 February 2018
The paper considers a problem of extrapolating functions of several variables. It is assumed that the values of the function of m variables at a finite number of points in some domain D of the m-dimensional space are given. It is required to restore the value of the function at points outside the domain D. The paper proposes a fundamentally new method for functions of several variables extrapolation. In the presented paper, the method of extrapolating a function of many variables developed by us uses the interpolation scheme of metric analysis. To solve the extrapolation problem, a scheme based on metric analysis methods is proposed. This scheme consists of two stages. In the first stage, using the metric analysis, the function is interpolated to the points of the domain D belonging to the segment of the straight line connecting the center of the domain D with the point M, in which it is necessary to restore the value of the function. In the second stage, based on the auto regression model and metric analysis, the function values are predicted along the above straight-line segment beyond the domain D up to the point M. The presented numerical example demonstrates the efficiency of the method under consideration.
© The Authors, published by EDP Sciences, 2018
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (http://creativecommons.org/licenses/by/4.0/).
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