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2015 A CONVERGENCE RESULT FOR MATRIX RICCATI DIFFERENTIAL EQUATIONS ASSOCIATED WITH $M$-MATRICES
Chun-Hua Guo, Bo Yu
Taiwanese J. Math. 19(1): 77-89 (2015). DOI: 10.11650/tjm.19.2015.4546

Abstract

The initial value problem for a matrix Riccati differential equation associated with an $M$-matrix is known to have a global solution $X(t)$ on $[0, \infty)$ when $X(0)$ takes values from a suitable set of nonnegative matrices. It is also known, except for the critical case, that as $t$ goes to infinity $X(t)$ converges to the minimal nonnegative solution of the corresponding algebraic Riccati equation. In this paper we present a new approach for proving the convergence, which is based on the doubling procedure and is also valid for the critical case. The approach also provides a way for solving the initial value problem and a new doubling algorithm for computing the minimal nonnegative solution of the algebraic Riccati equation.

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Chun-Hua Guo. Bo Yu. "A CONVERGENCE RESULT FOR MATRIX RICCATI DIFFERENTIAL EQUATIONS ASSOCIATED WITH $M$-MATRICES." Taiwanese J. Math. 19 (1) 77 - 89, 2015. https://doi.org/10.11650/tjm.19.2015.4546

Information

Published: 2015
First available in Project Euclid: 4 July 2017

zbMATH: 1357.34034
MathSciNet: MR3313405
Digital Object Identifier: 10.11650/tjm.19.2015.4546

Subjects:
Primary: ‎15A24‎, 34A12, 65F30

Rights: Copyright © 2015 The Mathematical Society of the Republic of China

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