Functional differentiation of integral operators of special form and some questions of the inverse interpolation
https://doi.org/10.29235/1561-2430-2021-57-4-401-416
Abstract
This article is devoted to the problem of operator interpolation and functional differentiation. Some information about the variational derivatives and explicit formulas for the exact solutions of the simplest equations containing the first variational derivatives of the required functional are given. For functionals defined on sets of functions and square matrices, various interpolating polynomials of the Hermitе type with nodes of the second multiplicity, which contain the first variational derivatives of the interpolated operator, are constructed. The presented solutions of the Hermitе interpolation problems are based on the algebraic Chebyshev system of functions. For analytic functions with an argument from a set of square matrices, explicit formulas for antiderivatives of functionals are obtained. The solution of some differential equations with integral operators of a special form and the first variational derivatives is found. The problem of the inverse interpolation of functions and operators is considered. Explicit schemes for constructing inverse functions and functionals, including the case of functions of a matrix variable, obtained using certain well-known results of interpolation theory, are demonstrated. Data representation is illustrated by a number of examples.
About the Authors
M. V. Ignatenko
Belarusian state University
Belarus
Belarus
Marina V. Ignatenko – Ph. D. (Physics and Mathematics), Associate Professor, Associate Professor of WebTechnologies and Computer Simulation Department
4, Nezavisimosti Ave., 220030, Minsk
L. A. Yanovich
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Leonid A. Yanovich – Corresponding Member, Dr. Sc. (Physics and Mathematics), Professor, Chief Researcher
11, Surganov Str., 220072, Minsk
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