Registration Number
0225U001878,
(0122U001223)
, R & D reports
Title
Theoretical and applied aspects of operator recovery and optimization of approximation of functions
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Асимптотично оптимальні відновлення операторів та їх застосування
Head
Parfinovych Nataliia V., Доктор фізико-математичних наук
Registration Date
10-02-2025
Organization
Oles Honchar Dnipro National University
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Development of new methods for optimizing the approximation of functions and operator recovery on incomplete and inaccurate information; development with the help of the created methods of technologies of compression, transfer and restoration of the damaged images, optimal computational algorithms and their application at processing of satellite data on monitoring of a terrestrial surface
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Purpose: to create a scheme for solving some problems in a general formulation. The paper proposes a general scheme for solving some approximation problems in a rather general formulation. The application of the proposed approach is illustrated by a number of examples, in particular, it is shown that many results in the field of Ostrowski type inequalities can be obtained by using standard reasoning. We develop asymptotically optimal methods for recovering the integration operator from function values at a finite number of points on classes of functions of many variables defined on a bounded star set and having bounded Lp-norm of the gradient. In particular, we generalise similar results for functions defined on convex sets. It is shown that the Boyanov-Naydenov problem on Sobolev classes with restrictions on local norms is equivalent to the problem of the exact constant in a Kolmogorov-type inequality with local norms. As a consequence, we obtain Kolmogorov type inequalities that are exact on cones generated by these Sobolev classes. A new model for satellite multiband image restoration is proposed in the form of an L1-control problem for a quasilinear parabolic equation with a nonlocal p[u]-Laplacian. For the purpose of application in satellite sensing of agricultural areas, a new approach to the region decomposition based on the anisotropic version of the Chan-Weese active contour model is developed. A new formulation of this problem in variable Sobolev spaces is proposed, a rigorous mathematical justification of the proposed optimisation problem is carried out, sufficient conditions for its solvability are established, and the corresponding optimality conditions are obtained.
Product Description
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Hnatushenko Volodymyr V.
Kovalenko Oleh V.
Kohut Petro І.
Kofanov Volodymyr O.
Menshova Viktoriia A.
Parfinovych Nataliia V.
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2025-02-10
