UNIVARIATE AND MULTIVARIATE POLYNOMIAL REGRESSION CONSTRUCTION FROM A REDUNDANT REPRESENTATION USING AN ACTIVE EXPERIMENT

Authors

DOI:

https://doi.org/10.20998/2079-0023.2020.01.02

Keywords:

multi-dimensional polynomial regression, normalized orthogonal polynomials of Forsythe, redundant representation, group method of data handling, cluster analysis, linear equalities

Abstract

We consider the problem of a multidimensional polynomial regression construction from a given redundant representation based on the results of an active experiment. Redundant representation means inclusion in it the members which are possibly absent in the structure of the studied regression. Thus, we have a problem not only to estimate the values of the unknown coefficients of multidimensional polynomial regression from the results of an active experiment, but also to eliminate the redundant members from its redundant representation. The solution to this problem is based on: (a) obtaining new properties of the coefficients of normalized orthogonal polynomials of Forsythe; (b) possibility of reducing the problem of estimating the unknown coefficients for nonlinear members of multivariate polynomial regression to the problem of estimating the coefficients for the set of univariate polynomial regressions and solving the corresponding systems of linear equalities; (c) using the method to eliminate the redundant members of multidimensional nonlinear polynomial regression which organically includes both the methodology of cluster analysis and the main idea of the group method of data handling – dividing the experimental data into two sets, one of which is not used to estimate unknown coefficients of multidimensional polynomial regression given by a redundant representation.

Author Biographies

Alexander Anatolievich Pavlov, National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute"

Doctor of Technical Sciences, Professor, National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Head of Department of Computer-Aided Management and Data Processing Systems; Kyiv, Ukraine

Maxim Nikolaevich Holovchenko, National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute"

National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Assistant of Department of Computer-Aided Management and Data Processing Systems; Kyiv, Ukraine

References

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How to Cite

Pavlov, A. A., & Holovchenko, M. N. (2020). UNIVARIATE AND MULTIVARIATE POLYNOMIAL REGRESSION CONSTRUCTION FROM A REDUNDANT REPRESENTATION USING AN ACTIVE EXPERIMENT. Bulletin of National Technical University "KhPI". Series: System Analysis, Control and Information Technologies, (1 (3), 9–13. https://doi.org/10.20998/2079-0023.2020.01.02

Issue

No. 1 (3) (2020)

Section

SYSTEM ANALYSIS AND DECISION-MAKING THEORY

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