Mashnitskyy M. Interpolation of multidimensional functions by difference methods

The research object is a process of interpolation functions of several variables. The research purpose is an increasing efficiency of interpolation functions by further development of difference numerical methods that improve the accuracy of interpolation and wide possibilities of numerical methods to solve problems of multidimensional interpolation. To research the defined purpose the numerical methods of interpolation, theory of difference schemes, matrix algebra theory and algorithms were used for developing mathematical models of multi-dimensional interpolation functions. Scientific novelty is following: a new approach for interpolation of multidimensional functions by difference methods was suggested, which unlike existing ones was based on the usage of multidimensional differences, that allows to develop the first multi-difference mathematical model for interpolation functions of several variables; further development of difference methods of interpolation was received, unlike the existing usage multidimensional differences, it allows to interpolate multidimensional function with a given accuracy near first values (multivariate model Newton's first formula), middle values (a multidimensional model formulas of Gauss, Bessel and Stirling) and the last values (multivariate model of Newton second formula) set intervals; mathematical models matrix interpolation difference methods of Newton and Gauss were first proposed, in comparison with the classical forms of models presentation, it allows to increase speed by parallelization process evaluations; the method of computation for interpolation functions of several variables by difference methods of Newton and Gauss was first proposed, unlike the classical method of computation, its usage of Horner's scheme allows to reduce the number of computing operations. The practical value consists in creation of the technique of proposed multidimensional interpolation mathematical models usage and development of algorithmic and software implementation for the proposed multidimensional interpolation methods. Implementation degree is in, that the thesis results were implemented in the software in companies "InnoVinnprom" (Vinnitsa, Ukraine) and of "SmartExe"(Ramat-Gan, Israel) and also in the education process of automation and information-measuring technology department of the VNTU. The application fields are multidimensional mathematical modeling systems, computer-aided design systems, computer graphics and other systems where the task of handling multivariate data takes place.