The paper presents the basic ideas of geometric objects approximation in multidimensional space by means the arcs of algebraic curves passing through given points, which is as follows. A special network of points with a dimension one less than the dimension of the space in which the simulated geometric object is located is formed. Taking into account the special properties the arcs of algebraic curves passing through the given points, a linear relationship between the parameters of the geometric object and the influence factors corresponding to the axes of the global coordinate system is established. Next, the nodes of the network are calculated such values of the response function, which provide the minimum value of the quadratic residual function. The proposed method allows to perform the generalization the method of least squares in the direction of increasing space dimension and, consequently, the number of investigated factors affecting the response function, which is especially important for modeling and optimization of multifactorial processes and phenomena.

approximation, geometric objects, multidimensional space, an arc of an algebraic curve, compartment the response surface, the response hypersurface

Konopatskiy Evgeny Viktorovich,  ,  Donbas National Academy of Civil Engineering and Architecture

Rotkov Sergey Igorevich,  ,  Nizhny Novgorod State University of Architecture and Civil Engineering