Publication detail

Discrete Riccati matrix equation and the order preserving property

ŠTOUDKOVÁ RŮŽIČKOVÁ, V.

English title

Discrete Riccati matrix equation and the order preserving property

Type

journal article in Web of Science

Language

en

Original abstract

It is known that if a symmetric matrix differential equation has the order preserving property and the matrix dimension is at least 2, then this equation is the Riccati matrix differential equation (see A.N. Stokes, A special property of the matrix Riccati equation, Bull. Austral. Math. Soc., 1974). In this paper we prove that a similar statement holds for discrete matrix equations as well. In the proof we use a new approach, in which we extend a discrete function to a continuous one by using the iteration theory and then apply the known result for the continuous case.

English abstract

It is known that if a symmetric matrix differential equation has the order preserving property and the matrix dimension is at least 2, then this equation is the Riccati matrix differential equation (see A.N. Stokes, A special property of the matrix Riccati equation, Bull. Austral. Math. Soc., 1974). In this paper we prove that a similar statement holds for discrete matrix equations as well. In the proof we use a new approach, in which we extend a discrete function to a continuous one by using the iteration theory and then apply the known result for the continuous case.

Keywords in English

Riccati matrix equation, order preserving property, symplectic matrix, iteration

Released

03.02.2021

Publisher

Elsevier

ISSN

0024-3795

Volume

618

Number

6

Pages from–to

58–75

Pages count

18

BIBTEX


@article{BUT168953,
  author="Viera {Štoudková Růžičková},
  title="Discrete Riccati matrix equation and the order preserving property",
  year="2021",
  volume="618",
  number="6",
  month="February",
  pages="58--75",
  publisher="Elsevier",
  issn="0024-3795"
}