Study On Some Splitting Iteration Methods And Accelerated Techniques For Two Classes Of Linear Matrix Equations

In this thesis,we discuss two classes of linear matrix equations,which are the following two issues:the splitting iteration algorithm and acceleration technology of continuous Sylvester equations AX+XB=C and linear matrix equation AXB=C.This kind of problem appears in many fields of science and engineering,such as control and system theory,signal processing,electric force system and so on.It is of great significance and practical background to construct these issues.The thesis consists of four chapters:In Chapter 1,we introduce the research background,research status and prepara-tory knowledge of two classes of linear matrix equations.In Chapter 2,firstly,the thesis introduces the continuous Sylvester equation AX+XB=C in detail through the introduction.Then we establish the GPSS iter-ation method,the inexact variant of the GPSS iteration method and the accelerated GPSS iteration method to solve the continuous Sylvester equation AX+XB=C.We also analyze the convergence of these three methods and prove the effectiveness of the method through numerical examples.Finally,we give a brief summary of this chapter.In Chapter 3,the first part of this chapter introduces the linear matrix equation AXB=C with the introduction.Then we propose the GPSS iteration method to solve the linear matrix equation AXB=C and analyzes the convergence of the GPSS iteration method.The inexact variant of the GPSS iteration method is added to solve the linear matrix equation and its convergence is also analyzed.On the basis of the GPSS iteration method,we establish the accelerated GPSS iterative method to solve the linear matrix equation AXB=C and its convergence is analyzed.By numerical examples illustrate the effectiveness of the method.We make a summary of this chapter at the end of this chapter.In Chapter 4,conclusion and prospect are given in chapter four.