Iteration Methods For Discrete Algebraic Riccati Matrix Equation

The linear and nonlinear matrix equation appear increasingly in the field of science and engineering calculation. There are a wide range of applications in control theory, transport theory, system theory, signal processing, dynamic pro-gramming, ladder network, statistical filtering and statistics. Hence, many scholars have studied the properties of the solution and the solution of matrix equation.This article mainly uses matrix Schur complement, the properties of matrix inverse, matrix inequalities and Schulz iteration to deal with discrete algebraic Ric-cati matrix equation. Meanwhile, we design a few inversion-free iteration methods and prove their convergence and the error analysis. Finally, we give some numeri-cal examples to demonstrate the effectiveness of our iteration methods.Main contents are as follows:In chapter one, some application background and research status about Lya-punov and Riccati matrix equation are introduced, and some marks and define are given in the text.In chapter two, we mainly use the properties of matrix Schur complement and the representation of partitioned matrix' inverse matrix to deal with discrete algebraic Riccati matrix equation, and give an inversion-free iteration method.Then we utilize the properties of matrix inequalities and matrix norm inequalities to prove its convergence. Finally, we give numerical examples to demonstrate the effectiveness of our iteration method.In chapter three, we will continue to improve the proposed algorithm in the previous chapter in a special kind of case. Firstly, we employ the representation of partitioned matrix' inverse matrix and identical deformation of partitioned matrix to give a reduced order iterative algorithm. Then we make use of Schulz iteration to replace matrix inverse. And we give some new iterative formats to completely avoid computing the matrix inversion. At last, numerical examples explain the effectiveness.