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Keywords:
Riccati matrix equation; order preserving property; symplectic matrix
Riccati matrix equation; order preserving property; symplectic matrix
Summary:
In this paper we recall discrete order preserving property related to the discrete Riccati matrix equation. We present results obtained by applying this property to the solutions of the Riccati matrix differential equation.
References:
[1] Coppel, W.A.: Disconjugacy. Lecture Notes in Mathematics, vol. 220, Springer-Verlag, Berlin-New York, 1971. Zbl 0224.34003
[2] Stokes, A.N.: A special property of the matrix Riccati equation. Bull. Austral. Math. Soc. 10 (1974), 245–253. DOI 10.1017/S0004972700040855
[3] Šimon Hilscher, R.: Asymptotic properties of solutions of Riccati matrix equations and inequalities for discrete symplectic systems. Electron. J. Qual. Theory Differ. Equ. No. 54 (2015), 1–16. MR 3391867
[4] Štoudková Růžičková, V.: Discrete Riccati matrix equation and the order preserving property. Linear Algebra Appl. 618 (2021), 58–75. MR 4213703
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