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Information × Registration Number 0223U002055, 0122U001223 , R & D reports Title Theoretical and applied aspects of operator recovery and optimization of approximation of functions popup.stage_title Head Parfinovych Nataliia V., Доктор фізико-математичних наук Registration Date 07-02-2023 Organization Oles Honchar Dnipro National University popup.description2  The object of research is the optimal approximation of operators and functional classes by certain approximation devices; optimal algorithms for restoring operators based on incomplete and inaccurate information; development of optimal numerical algorithms for image compression, transmission and processing technology and their application to satellite data recovery. The purpose of the work is to create new methods for optimizing the approximation of functions and restoring operators based on incomplete and inaccurate information; development with the help of created methods of technologies of compression, transmission and restoration of damaged images, optimal computing algorithms and their application in processing satellite data for monitoring the earth's surface. Research methods are modern methods of theory of functions, theory of approximation, theory of optimal algorithms, mathematical and functional analysis. On the class of elements of the normalized space, the problem of optimal recovery based on imprecisely specified information is solved. Estimates of the deviation of integral operators operating in function spaces with values ​​in semi-linear spaces are obtained. Exact inequalities of the Kolmogorov-Remez type are obtained for periodic functions of low smoothness, which evaluate the L_q-norm of the intermediate derivative through the L_p-norm of the function and the uniform norm of its senior derivative. A two-level variational model in Sobolev-Orlych spaces with non-standard conditions for the growth of the objective functional is proposed for solving the problem of spatio-temporal interpolation of satellite multi-spectral images. The results are fed into the reconstruction of Landsat satellite images. The results are recommended for use in the areas of research: extreme problems of analysis and approximation theory, computational mathematics, theory of ill-posed problems, as well as satellite data recovery. Product Description popup.authors Hnatushenko Volodymyr V. Kovalenko Oleg V. Kogut Petro І. Kofanov Volodymyr O. Parfinovych Nataliia V. popup.nrat_date 2023-02-07 Close