University Of Tehran Press Journal of Algorithms and Computation 2476-2776 Articles in Press 2022 08 29 An iterative method and maximal solution of Coupled algebraic Riccati equations 88681 10.22059/jac.2022.345099.1174 EN Hajar Alimorad Jahrom University Journal Article 2022 06 27 Coupled Riccati equation has widely been applied to various engineering areas such as jump linear quadratic problem, particle transport theory, and Wiener–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&#039;s method.