VARIATIVE GEOMETRIC ALGORITHMS FOR MODELING MULTIFACTOR PROCESSES

Abstract

The work is investigated by the influence of variable geometric algorithms in modeling multifactor processes using multidimensional interpolation. Geometric models of multifactorial processes obtained using multidimensional interpolation inherent variability, which is a consequence of the multiplicity of the choice of reference lines during the development of geometric modeling schemes. At the same time, all possible variations of geometric interpolyns are fully satisfying the initial data. It has been established that the number of variations of geometric schemes directly depends on the number of current parameters and the dimension of the space in which the simulated geometrical object is located. Thus, a variable approach to geometrical modeling of multifactor processes generates a number of scientific tasks, the main one is the need to determine the effect of the variability of geometric algorithms on the final results of the computational experiment and, as a result, the choice of the best modeling results. To this end, the article presents the studies of variable geometric algorithms and computational experiments on the example of 2-parametric geometric interpolyns. A classification of 2-parametric geometric interpolytesses, which were conditionally divided into 3 types. Depending on the geometric scheme of constructing interpolynta, the square geometric scheme, a rectangular geometric scheme, a mixed geometric scheme. As a result of computational experiments, it was found that for a square geometric scheme, the variability does not affect the final results, in rectangular geometric schemes, the variability has a slight influence, and mixed geometric schemes may have significant differences and require additional research to select the highest quality geometric process model. Comparison of geometric models were performed by the methods of scientific visualization by overlaying the response surfaces on each other.