Ivanin D. Methods and Algorithms for the Recovery of Functions Based on the Binary Data Refilling.

The dissertation is devoted to the solution of some problems of the recovery of functions of one or two variables. For the functions of one variable linear recovery methods based on the simultaneous data refilling at the intermediate points and their smoothing at the initial points are developed. The guaranteed estimations of the deviation of polygons or splines and their derivatives based upon the data of k-step of refilling from the boundary function and its relative derivatives are obtained. We show them to be the linear methods of a summatory type and investigate the approximation and other properties of these methods. Obtained results are extended to the cases of the re-covery of the function of two variables. It is shown that the de-veloped methods may be used to recover functions of one or two variables. Specifically, these methods have been applied to con-struct deviation tables, to create algorithms for the sharing transmission of information and to construct new types of wave-lets.