Numerical Algorithm For Sylvester Matrix Equation

Sylvester matrix equations and linear equations play an important role in many fields, such as scientific computing and engineering application. In fact, many problems in control system theorem, power system, signal processing, image restoration, and numerical solution of differential equation can be converted to matrix equation or linear equation finally. Hence, it is significantly important to develop efficient algorithms to solve these two kinds of equations since they can be applied in so many areas.The thesis mainly focus on algorithms to solve Sylvester matrix equations and general linear equations. Firstly, we apply triangle splitting iteration algorithm to solve Sylvester matrix equation. We proof the convergence property of this algorithm. More-over, the detailed computation results show the efficiency of the algorithm. Secondly, we exploit a new direct method to solve general linear equations. We show better stability and less computation cost of the method theoretically and numerically.