On The Convergence Rate Analysis Of The OROD Method For Solving The Matrix Equation

In 2004, Peng in her doctoral dissertation presented an efficient orthogonal residual and orthogonal direction method(OROD) for solving matrix equations. She showed that the OROD method possesses finite termination property. However, its convergence rate is not known. In this paper, we prove that this method has Q- linear convergence rate and some minimization properties for several matrix equations such as AX=B, CAXB=,AX=B, XC=D. Moreover, we do some numerical experiments to show these theoretical results.Chapter 1 introduces the background and some preliminary knowledge.Chapter 2 investigates the convergence rate of the OROD method for the matrix equation AX=B.We prove its Q- linear convergence rate and study its some optimization properties.Chapter 3 discusses the convergence rate of the OROD method for the matrix equation CAXB=. We prove its Q- linear convergence rate and study its some optimization properties.Chapter 4 studies the convergence rate and some properties of the OROD method for the matrix equation AX=B, XC=D. We prove its Q- linear convergence rate and study its some optimization properties.