Discrete Riccati matrix equation and the order preserving property

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2021-02-03
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Elsevier
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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.
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LINEAR ALGEBRA AND ITS APPLICATIONS. 2021, vol. 618, issue 6, p. 58-75.
https://www.sciencedirect.com/science/article/pii/S0024379521000409
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Peer-reviewed
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2023-02-03
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en
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Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
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