Development of a numerical method for solving optimization problems approximation of the function given approximately and its derivatives based on the variational approach - Igor Naats; Victoria Igorevna Naats; Elena Yartseva (Наука. Инновации. Технологии)
Introduction: the presented work continues the authors' research on the methods of the theory of approximation of functions of a real variable, given approximately, on the basis of their representation by integrals. Materials and methods of research: the paper studies the methods of representation of functions given approximately by their singular integrals in relation to the approximation problems, both the functions themselves and their derivatives. The problem of "recovery" of the function from approximate data is formulated, the basic concepts, definitions and approaches to its solution are briefly described. A numerical method for solving optimization problems of function approximation from approximate data is developed. The construction of the corresponding computational algorithm is carried out. The problem of «recovery» of derivatives of the function under study and approaches to its solution are considered. Research results and their discussion: a possible application of this theory is the problem of computational mathematics associated with the operators of generalized differentiation of summable functions and finding the so-called weak solutions for boundary value problems of mathematical physics. The practical significance of the results is that the proposed methods and approaches can be used in applied problems of the theory of approximation of functions, problems of applied analysis and boundary value problems of mathematical physics, using approximately given initial data obtained in the course of physical experiments or empirical functions.