The Problem of Restoring the Unit of Approximation in the Model for Studying Functional Dependence from Approximate Data

Abstract

In this paper, we demonstrate the application of the analytical apparatus of representing functions by their singular integrals for developing numerical methods by interpreting approximate data in the problem of correctly restoring the studied functional dependencies. Such approach significantly extends the substantive basis of the apparatus for approximating functions in problems, where it is necessary to build a model of the functional dependence, which depends on approximate data. The main goal of this article is to provide the restoring of the real-valued functions f= {f(x0), f(x1),.., f(xm) }, associated with discrete sequence of points {xk}k=0m on [a, b], using generalized kernel (Knf) (x). We will demonstrate the theoretical calculations of restoring of the unit approximation, which is able to increase the accuracy of approximations. In the end of our research, the application of proposed approximation is used for solving optimization problem, where rising of the accuracy with minimal time computations plays an important role.