Geodesic
On the theory of operator interpolation in spaces of rectangular matrixes
Journal of the Belarusian State University. Mathematics and Informatics, Tome 3 (2022), pp. 91-106
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The problem of constructing and studying interpolation operator polynomials of an arbitrary fixed degree, defined in spaces of rectangular matrices, which would be generalisations of the corresponding interpolation formulas in the case of square matrices, is considered. Linear interpolation formulas of various structures are constructed for rectangular matrices. Matrix polynomials, with respect to which the resulting interpolation formulas are invariant, are indicated. As a generalisation of linear formulas, formulas for quadratic interpolation and interpolation by polynomials of arbitrary fixed degree in the space of rectangular matrices are constructed. Particular cases of the obtained formulas are considered: when square matrices are chosen as nodes or when the values of the interpolated function are square matrices, as well as the case when both of these conditions are satisfied. For the last variant, the possibilities of different and identical matrix orders for nodes and function values are explored. The obtained results are based on the application of some well-known provisions of the theory of matrices and the theory of interpolation of scalar functions. The presentation of the material is illustrated by a number of examples.
Keywords: pseudo-inverse matrix; skeletal decomposition of a matrix; function of a matrix; matrix polynomial; operator interpolation. 
@article{BGUMI_2022_3_a7,
     author = {M. V. Ignatenko and L. A. Yanovich},
     title = {On the theory of operator interpolation in spaces of rectangular matrixes},
     journal = {Journal of the Belarusian State University. Mathematics and Informatics},
     pages = {91--106},
     year = {2022},
     volume = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/BGUMI_2022_3_a7/}
}
TY  - JOUR
AU  - M. V. Ignatenko
AU  - L. A. Yanovich
TI  - On the theory of operator interpolation in spaces of rectangular matrixes
JO  - Journal of the Belarusian State University. Mathematics and Informatics
PY  - 2022
SP  - 91
EP  - 106
VL  - 3
UR  - http://geodesic.mathdoc.fr/item/BGUMI_2022_3_a7/
LA  - ru
ID  - BGUMI_2022_3_a7
ER  - 
%0 Journal Article
%A M. V. Ignatenko
%A L. A. Yanovich
%T On the theory of operator interpolation in spaces of rectangular matrixes
%J Journal of the Belarusian State University. Mathematics and Informatics
%D 2022
%P 91-106
%V 3
%U http://geodesic.mathdoc.fr/item/BGUMI_2022_3_a7/
%G ru
%F BGUMI_2022_3_a7
M. V. Ignatenko; L. A. Yanovich. On the theory of operator interpolation in spaces of rectangular matrixes. Journal of the Belarusian State University. Mathematics and Informatics, Tome 3 (2022), pp. 91-106. http://geodesic.mathdoc.fr/item/BGUMI_2022_3_a7/

[1] F. R. Gantmakher, Teoriya matrits, Nauka, Moskva, 1967, 575 pp.

[2] Ya. R. Magnus, Kh. Neidekker, Matrichnoe differentsialnoe ischislenie s prilozheniyami k statistike i ekonometrike, Fizmatlit, Moskva, 2002, 496 pp.

[3] V. L. Makarov, V. V. Khlobystov, L. A. Yanovich, Methods of operator interpolation, Pratsi institutu matematiki NAN Ukraini, 83, Іnstitut matematiki NAN Ukraini, Kiiv, 2010, 517 pp.

[4] L. A. Yanovich, M. V. Ignatenko, Osnovy teorii interpolirovaniya funktsii matrichnykh peremennykh, Belaruskaya navuka, Minsk, 2016, 281 pp.

[5] L. A. Yanovich, M. V. Ignatenko, Interpolyatsionnye metody approksimatsii operatorov, zadannykh na funktsionalnykh prostranstvakh i mnozhestvakh matrits, Belaruskaya navuka, Minsk, 2020, 476 pp.