Iarmosh O. Interpolation, interlination and blending approximation of functions in modeling social and economic processes

Object is the mathematical modeling of optimal processes in services by developed theory of approximation of two variables functions by sums of products of different variables functions. The purpose is construction of mathematical models of social and economic processes, particularly with the use of interpolation, interlination and blending approximation, and research of constructed approximation operators and the error estimation of approximation of two variables functions. Methods: approximation theory of functions, theory of variation calculus, functional analysis, decision making, constructing programs by means of MathCad. The results have theoretical value in the theory of approximation of two variables functions. Based on the methods and applications can be obtained approximation of two variables function, perform calculations approximation errors by operators acting on one variable; conduct simulations of social and economic processes and management decisions. Scientific novelty. 1. Were further developed the theory of approximation of two variables functions by interlination and blending approximation of functions. 2. First obtained and investigated expression images MLS-residue approximation of two variables functions defined on the system traces perpendicular lines, depending on the MLS-residual approach for one variable. 3. First formulated and proved a theorem on error estimates spline interlination the case of default trace errors. 4. First created and studied a general method for constructing a mathematical model in the form interlination functions for the formation of the university students' contingent, depending on its rating and price study, and using the first degree spline interpolation on the triangulated grid nodes and global interpolation formulas. 5. First created and studied mathematical models based educational services for the ranking universities at which the maximum of enrolled students. The results were partly used in carrying out the research work number 09- 03ДБ (№ ДР 0108U010843) and introduced to the course "High Mathematics", which is confirmed by the relevant act. The results are the basis for solving important scientific problems in computing and seismic tomography, digital processing of multidimensional signals, constructing mathematical models of the spatial distribution of minerals and can be used in modeling various social and economic processes and phenomena.