# On the Convergence of the Accelerated Riccati Iteration Method

## TL;DR

This paper proves the convergence and desirable properties of the accelerated Riccati iteration method for solving the continuous coupled algebraic Riccati equation, addressing open problems and demonstrating its advantages over standard methods.

## Contribution

It provides a comprehensive convergence analysis of the accelerated Riccati iteration method, confirming its effectiveness and advantages in solving CCARE.

## Key findings

- The method produces monotonic and bounded sequences.
- It can determine the existence of solutions to CCARE.
- It converges faster than the regular Riccati iteration method.

## Abstract

In this paper, we establish results fully addressing two open problems proposed recently by I. Ivanov, see Nonlinear Analysis 69 (2008) 4012--4024, with respect to the convergence of the accelerated Riccati iteration method for solving the continuous coupled algebraic Riccati equation, or CCARE for short. These results confirm several desirable features of that method, including the monotonicity and boundedness of the sequences it produces, its capability of determining whether the CCARE has a solution, the extremal solutions it computes under certain circumstances, and its faster convergence than the regular Riccati iteration method.