Dementiev V. Interpolation of almost periodic functions by trigonometric splines in problems of discrete data processing.

The object of research is the process of interpolation of almost periodic functions in problems of processing multidimensional discrete data. The study dedicated to improve the accuracy of interpolation of discrete almost periodic functions on the basis of a new method of trigonometric spline interpolation and expanding its field of application in multiparameter function. To achieve this goal uses mathematical models and methods for interpolation of almost periodic functions in the technical problems of processing multidimensional discrete data. The novelty is that first proposed a new method of trigonometric spline interpolation, allowing interpolation to increase the accuracy while maintaining the number of computational operations, compared with similar methods for discrete data that are almost periodic in nature. A two-dimensional and multi-dimensional mathematical model for a new method of trigonometric spline interpolation, which, unlike existing permit interpolate discrete almost periodic functions of many variables that you can apply the proposed method for a wide range of practical problems of arbitrary measurability. A matrix model developed by the method of trigonometric spline interpolation for almost periodic functions specified number of independent variables, unlike the existing math forms the basis for the algorithm creates a mathematical model developed method and enables you to increase the speed of interpolation by parallel matrix operations in multithreaded processor devices. The practical value lies in creating methods of using the proposed mathematical model of multidimensional interpolation by trigonometric splines and the development of algorithmic and software to implement a multidimensional interpolation by the proposed methods. The degree of implementation - the results of the thesis implemented in software company "Spilna sprava" (Vinnitsa, Ukraine), Enterprise "Enerhooblik" (Vinnitsa, Ukraine), and also used in the learning process of the department of automation and information-measuring equipment VNTU . Area (region) use - systems of multivariate mathematical modeling of almost periodic discrete data, Computer Graphics, processing of discrete signals.