On the theory of interpolation of functions on sets of matrices with the Hadamard multiplication
https://doi.org/10.29235/1561-2430-2022-58-3-263-279
Abstract
This article is devoted to the problem of interpolation of functions defined on sets of matrices with multiplication in the sense of Hadamard and is mainly an overview. It contains some known information about the Hadamard matrix multiplication and its properties. For functions defined on sets of square and rectangular matrices, various interpolation polynomials of the Lagrange type, containing both the operation of matrix multiplication in the Hadamard sense and the usual matrix product, are given. In the case of analytic functions defined on sets of square matrices with the Hadamard multiplication, some analogues of the Lagrange type trigonometric interpolation formulas are considered. Matrix analogues of splines and the Cauchy integral are given on sets of matrices with the Hadamard multiplication. Some of its applications in the theory of interpolation are considered. Theorems on the convergence of some Lagrange interpolation processes for analytic functions defined on a set of matrices with multiplication in the Hadamard sense are proved. The results obtained are based on the application of some well-known provisions of the theory of interpolation of scalar functions. Data presentation 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 Departmen
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 of the
National Academy of Sciences of Belarus, Dr. Sc. (Physics
and Mathematics), Professor, Chief Researcher
11, Surganov Str., 220072, Minsk
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