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A number of results related to the optimal recovery of finite differences based on approximately known information is discussed: - the problem of simultaneously recovering the operators of all differences of a sequence in the Euclidean norm within a class of sequences with a bounded n-th divided difference based on an approximately known Fourier transform of the sequence on a segment; - the problem of recovering the operator of a k-th divided difference of a sequence in the Euclidean norm from imprecisely specified divided differences of other orders; - the problem of the best recovery of the powers of a finite-dimensional operator based on some approximately known powers. In all of these problems, recovery methods are constructed within their respective classes. The problems addressed in this work are applicable in scenarios such as reconstructing the body temperature in heat conduction equations or recovering the solution of a system of ordinary differential equations.
Abramova et al. (Mon,) studied this question.