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Optimal Approximation for Multidimensional Nonlinear Point Data Sets

Authors:
Rudolf Neydorf
Dean Vučinić
Victor Poliakh

Keywords: xperimental data; fragments; math modeling; approximation; error; evoluti

Abstract:
The mathematical modelling of complex physical processes (objects) is based on the approximation of their experimental output variables (point data sets). It is well known that the respective mathematical models are multidimensional and significantly nonlinear, thus various mathematical methods were developed to approximate the experimental point data, each having its own inherent approximation advantages and disadvantages. However, these methods did not take into account the data structural and parametric characteristics. and thus motivated this research to develop a more universal approximation methodology to this kind of problem. The applied approximation method, named Cut-Glue Approximation, takes into account any data order and/or any nonlinear dependency based on 3 principles: fragmentation of the initial data approximated by known methods; high-precision analytical approximation of local fragments; multiplicative analytic fragmentation of local functions isolated in the factor space. This paper considers the second stage of the Cut-Glue Approximation - analytical approximation of local fragments. The direct advantage of this approximation is the resulting mathematical model differentiability, which enables their analytical investigation, appropriate for modelling complex dynamical systems.

Pages: 1 to 7

Copyright: Copyright (c) IARIA, 2019

Publication date: September 22, 2019

Published in: conference

ISSN: 2308-4499

ISBN: 978-1-61208-737-5

Location: Porto, Portugal

Dates: from September 22, 2019 to September 26, 2019