Two-sided estimation of linear approximation error second - order hypersurfaces

Abstract

The following aspects of multidimensional space are considered in the article. The parametrizations of the hypersurface of the second order are considered, which allow visualizing them in the process of discretization. The development of the principle of vector modeling for displaying objects of multidimensional space on a two-dimensional plane made it possible to visually display the solution to the problem of linear approximation of a second-order hypersurface. The proposed method for discretizing a second-order hypersurface makes it possible to create a simple algorithm for its linear ash-approximation, which is the basis for solving the linear programming problem in automatic mode. The developed method of two-sided estimation of the error in the case of linear approximation of the second-order hypersurface allows us to present the problem of determining the bearing capacity of structures as a linear programming problem.