Author:
Xiong Hao,Huang Jingpin,Zhang Shanshan,Wang Yun
Abstract
Abstract
In this paper, we study the matrix equation X+A
*
(R+B
*
XB)
-t
A=Q (0<t⩽1), where A, B, R, Q are matrices of appropriate size and R, Q are both positive definite matrices. Based on the fixed point theorem, we suggest four iterative algorithms for solving this equation and prove that the suggested iterative algorithms are convergent with proper conditions. What’s more, the conditions for the existence of the positive definite solution are given. The convergence analysis of the suggested algorithms is established. Some numerical examples are presented to illustrate the convergence behaviour of the various algorithms.
Subject
General Physics and Astronomy