University of TehranJournal of Algorithms and Computation2476-2776Articles in Press20220829An iterative method and maximal solution of Coupled algebraic Riccati equations8868110.22059/jac.2022.345099.1174ENHajarAlimoradJahrom UniversityJournal Article20220627Coupled Riccati equation has widely been applied to various engineering areas such as jump linear quadratic problem, particle transport theory, and Wienerâ€“Hopf decomposition of Markov chains. In this paper, we consider an iterative method for computing Hermitian solution of the Coupled Algebraic Riccati Equations (CARE) which is usually encountered in control theory. We show some properties of this iterative method. Furthermore, it will also be demonstrated that the maximal solution can be obtained numerically via a certain linear or quadratic inequalities optimization problem. Numerical examples are presented and the results are compared.<br />
Coupled algebraic Riccati equations; Maximal solution; Positive semidefinite matrix; Remodified Newton's method.