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In this paper, the geometric theory of multidimensional interpolation was further developed. It has been established that the geometric models of multivariate processes obtained using multidimensional interpolation are characterized by variability, which is a consequence of the multiplicity of choice of reference lines in the process of developing a geometric modeling scheme. At the same time, all possible variations of geometric interpolants fully satisfy the initial experimental and statistical data, but have different curvature between the node points of the interpolation. As the dimension of the space increases, the number of variations increases significantly. The variable approach to geometric modeling of multifactorial processes generates a number of scientific problems that require further research, such as: comparison of geometric objects of multidimensional space, development of criteria for choosing the best solutions, construction of averaged geometric objects as one of the tools for optimizing the results of modeling, etc. The article also presents the results of a computational experiment on geometric modeling of the dependence of the physical and mechanical properties of fine-grained concrete on the composition of the combined aggregate based on variable point algorithms with the subsequent construction of an averaged response surface, the current point of which is the center of gravity of a multidimensional tetrahedron, for which the dimension of space depends on the amount possible interpolation options. |
