On the Iterative Methods for the Solution of Three Types of Nonlinear Matrix Equations

In this paper, we investigate the iterative methods for the solution of different types of nonlinear matrix equations. More specifically, we consider iterative methods for the minimal nonnegative solution of a set of Riccati equations, a nonnegative solution of a quadratic matrix equation, and the maximal positive definite solution of the equation X+A*X-1A=Q. We study the recent iterative methods for computing the solution to the above specific type of equations and propose more effective modifications of these iterative methods. In addition, we make comments and comparisons of the existing methods and show the effectiveness of our methods by illustration examples.

Automated summary

This paper investigates iterative methods for solving various types of nonlinear matrix equations. Specifically, it focuses on iterative methods for finding the minimal nonnegative solution of a set of Riccati equations, the nonnegative solution of a quadratic matrix equation, and the maximal positive definite solution of the equation X+A*X-1A=Q. The paper studies recent iterative methods for solving these specific types of equations, proposes more effective modifications to these methods, and demonstrates their effectiveness through illustrative examples.