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Information × Registration Number 0224U001888, 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 01-02-2024 Organization Oles Honchar Dnipro National University popup.description2 The object of research is the best 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 aim 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. The problem of the best approximation of closed operators by linear bounded operators in the Hilbert space is solved under the assumption that the operators preserve the orthogonality of the basis of the Hilbert space. A generalization of the Korneychuk-Stechkin lemma for functions with values in L-spaces is obtained. The Boyanov-Naidyonov problem for positive (negative) parts of functions on classes of functions with a given comparison function with restrictions on the norms of positive (negative) parts of functions is solved. The proposed variational model of optical flow reproduction for temporal interpolation of static images. The results are involved in the restoration of optical flows based on data from the Sentinel-2 satellite. 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 Gnatushenko Volodymyr V. Kovalenko Oleg V. Kogut Petro І. Kofanov Volodymyr O. Parfinovych Nataliia V. popup.nrat_date 2024-02-01 Close