Yudin O. Interpolation of multidimensional functions in space and time

An object of research is the process of finding interpolation function that expresses the relationship between analytical arguments and values of the experimental data in a multidimensional space. The purpose of the research is to improve and expand the application of interpolation methods to make possible the interpolation of values in multidimensional space with time. Scientific innovation is that the first proposed settlement of the problem of interpolation using NURBS-curves, the first modification of the method steepest descent to minimize the functions of several variables that have gaps in partial derivatives, first proposed approach and the mathematical model of linearization spherical interpolation based on the use of linear interpolation with a given accuracy, the first method of interpolation curves bicubical splines for interpolation of surfaces based on Katmull-Rome spline. The practical significance of the results is that the methodology of construction of interpolation functions using NURBS-curves; developed algorithm and software implementation methods of functions optimization that have discontinuities partial derivatives, developed a method of linearization by the time parameter of spherical interpolation for the sphere in space of any order with a given maximum allowable error, algorithm and program to enlarge the images using the interpolation of missing points of the image based on bicubical splines of Katmull-Rome with high speed. Level of integration - the researches integrated in the Basin management of water resources of Southern Bug river and in the study process. A sphere of use data processing systems, computer-aided design systems and computer graphics.