“…If, moreover, requires that the local evaluation results were represented generally smooth function that necessitates a smooth interfacing of said polynomials, the least squares problem is converted into a quadratic optimization problem with constraints in the general case, as the type of equality and inequality [4 -6]. In the considered setting, the problem of local evaluation or analysis -is the problem of recovering a continuous function or signal from discrete data, the parameters of which are the size of the intervals of data and analysis, as well as the magnitude of the shift interval analysis of data relative to the interval [4,5]. The values of these parameters significantly affect the nature of the results of the signal processing, for example, that allows them to multi-scale analysis and smoothing.…”