A precondition conjugate gradient method for solving the Sylvester matrix equation

摘要

The conjugate gradient method is a powerful solution scheme for solving a class of matrix equations. For example, the Sylvester equation, of the form: AX+XB=C. However, as we known it is unstable. In this paper, we first deal with the coefficient matrix and then utilize the conjugate gradient algorithm for it By this iterative, some numerical experiments are also reported, as we can see, as long as giving any initial matrix X0, a solution X can be obtained within finite iteration steps in the absence of round-off errors. These examples illustrate the convergence properties of the algorithm and the precondition method is more.