Geometric modeling of multifactor processes and phenomena by the multidimensional parabolic interpolation method
E. V. Konopatskiy, A. A. Bezditnyi
Abstract
Abstract The paper presents the results of multidimensional parabolic interpolation studies, (one of the special cases of the multidimensional interpolation method), applied to solve problems of modelling multifactor processes and phenomena using geometric objects of multidimensional affine space. The authors describe the technique of geometric model tree forming of the process under study and its analytical description based on computational point algorithms with subsequent implementation on a computer. Such an approach makes it possible to effectively use multidimensional interpolation instead of multidimensional approximation (based on the least squares method) for solving problems of mathematical and computer modelling of multifactor 3-level processes and phenomena of animate and inanimate nature, technology, economy, construction, and architecture The study gives an example of multidimensional parabolic interpolation application to simulate the dependence of the fine-grained tar-polymer concrete compressive strength on 4 factors: tar viscosity, polyvinyl chloride dropout concentration in coal tar, activator concentration on the mineral powder surface and temperature, followed by optimization of the composition and operating conditions road pavement.