Detail publikace

Discrete Riccati matrix equation and the order preserving property

ŠTOUDKOVÁ RŮŽIČKOVÁ, V.

Anglický název

Discrete Riccati matrix equation and the order preserving property

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

en

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova anglicky

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

Vydáno

03.02.2021

Nakladatel

Elsevier

ISSN

0024-3795

Ročník

618

Číslo

6

Strany od–do

58–75

Počet stran

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"
}