Preconditioned Technology For Solving Sylvester Matrix Equations

Sylvester matrix equation has been widely applied in the field of scientific computing and engineering technology,such as system theory,dynamic system,model reduction,the optimal approximation problem of matrix,numerical solutions of differential equations,finite element model updating,image restoration and fluid mechanics.So,it is of great theoretical and practical significance to study the numerical solution of the Sylvester matrix equation.In this paper,two preconditioned techniques are presented to solve the numerical solution of continuous Sylvester matrix equation.Firstly,we obtain a preconditioned normal and skew-Hermitian(PNSS)iterative method by analyzing the NSS iterative method,and analyze its convergence.An inexact PNSS(IPNSS)iteration method is established,the effectiveness and superiority of this method is verified by several numerical experiments.This article is divided into four chapters,which are organized as follows:In Chapter 1,we introduce the background of the research,current research status,some related theoretical knowledge of Sylvester matrix equation numerical solution method and the main contents of this paper.In Chapter 2,we obtain a preconditioned method(PNSS)iterative method for solving the Sylvester matrix equation by analyzing the NSS iterative method.It is proved that this method will converge under certain conditions.In addition,in order to reduce the computational complexity of the algorithm,we also propose an inexact PNSS method.Several numerical experiments show that the PNSS iterative algorithm and the IPNSS iterative algorithm are more effective.In Chapter 3,we propose the lopsided PPSS iteration method for solving the continuous Sylvester matrix equation,and analyze its convergence.Several numerical experiments also demonstrate the effectiveness of the new method.In the end,we provide some conclusions and we discuss possible research work.