Nechuiviter O. Cubature formulas of the computing of integrals of highly oscillating functions of three variables using interflatation of functions

The thesis is dedicated to the improvement of mathematical models of digital signal processing and imaging by the example of constructing cubature formulas of approximate calculation of integrals of highly oscillatory functions of three variables. The feature of the proposed cubature formulas is using the input information about function as a set of traces of function on planes or a set of traces of function on lines or as a set of values of the function in the points. Cubature formulas are based on Failon method and also on the application of interlineation and interflatation theory. It was given the errors of estimation for the approximation of integrals of functions in the classes of Lipschitz, Helder. Optimality by the order of accuracy of the cubature formulas was proved on the class of differentiable functions. In this thesis a cubature formula is built using Lagrange polynomial operators of interflatation and the optimal choice of planes. It is proved that the proposed cubature formula is optimal by order of accuracy on the class of differentiated functions. Cubature formulas with using the input information as a set of values of the function in the points are effective. They use a minimal amount of input information and the time spent on the computation compared to classical formulas to achieve the same accuracy.