Efficient Computations for Solving Algebraic Riccati Equations by Newton's Method

Based on equivalent formulas for generalized continuous- and discrete-time algebraic Riccati equations (AREs), improved algorithms are proposed for solving such equations using Newton's method. The residual and closed-loop matrices needed by Newton solvers are efficiently computed, in order to reduce the computational effort per iteration. Newton algorithms are suitable for solving large AREs with dense matrices, and especially for improving the accuracy of the solutions provided by other algorithms.