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ŠTOUDKOVÁ RŮŽIČKOVÁ, V.
Original Title
Discrete Riccati matrix equation and the order preserving property
Type
journal article in Web of Science
Language
English
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.
Keywords
Riccati matrix equation, order preserving property, symplectic matrix, iteration
Authors
Released
3. 2. 2021
Publisher
Elsevier
ISBN
0024-3795
Periodical
LINEAR ALGEBRA AND ITS APPLICATIONS
Year of study
618
Number
6
State
United States of America
Pages from
58
Pages to
75
Pages count
18
URL
https://www.sciencedirect.com/science/article/pii/S0024379521000409
Full text in the Digital Library
http://hdl.handle.net/11012/201671
BibTex
@article{BUT168953, author="Viera {Štoudková Růžičková}", title="Discrete Riccati matrix equation and the order preserving property", journal="LINEAR ALGEBRA AND ITS APPLICATIONS", year="2021", volume="618", number="6", pages="58--75", doi="10.1016/j.laa.2021.01.021", issn="0024-3795", url="https://www.sciencedirect.com/science/article/pii/S0024379521000409" }