Search academic texts

Information × Registration Number 0219U004154, 0116U002256 , R & D reports Title Theory of Optimal Algorithm and Extremal Problems of Analysis popup.stage_title Head Parfinovych Natalia Viktorivna, Registration Date 04-04-2019 Organization Oles Honchar Dnipro National University popup.description2 Research object is the problem of recovering with incomplete and inaccurately given information, optimal recovery of solutions of boundary value problems for partial differential equations, inequalities for derivatives, Remez type inequalities, Boyanov-Naidenov and Kolmogorov problems. The work purpose is to solve problems of optimal recovery of operators on certain classes according to information given with an error, optimal recovery of solutions of boundary problems for partial differential equations, to obtain new exact inequalities for derivatives of univariate functions in different metrics and new exact inequalities of Ostrovsky type for multivariate functions, to solve the Boyanov - Naidenov problem and the Kolmogorov problem on certain classes of functions. Research approaches include modern methods of Function Theory, Approximation Theory, Theory of Optimal Algorithms, Mathematical and Functional Analysis. We found the solution of the problem of recovery of sufficiently arbitrary integral operators under incompleter information with an error. The obtained results are applied to finding the optimal recovery method, and we calculate the optimal error for solutions of some integral equations and solutions of boundary problems of partial differential equations. We obtained the solutions of the Boyanov-Naidenov and Kolmogorov problems for some classes of functions. We obtained new Remez-type inequalities of various metrics, as well as Remes-Nadgy-type inequalities for Sobolev classes of differentiable periodic functions and Remez-Nikolski type inequalities for trigonometric polynomials and polynomial splines.New Ostrovski type inequalities for multidimensional sets and functions of several variables of bounded variation are obtained. These results are important because they form the basis for solving important extremal problems of analysis and approximation theory. The areas of application are extremal problems of analysis and approximation theory, computational mathematics, the theory of ill-posed problems. Product Description popup.authors Коваленко Олег Вікторович Кофанов Володимир Олександрович popup.nrat_date 2020-04-02 Close