SOR FOR AX-XB=C

We consider a new approach to the block SOR method applied to linear systems of equations which can be written as a matrix equation AX - XB = C. Such systems arise, for example, from finite difference discretizations of separable elliptic boundary value problems on rectangular domains. On one hand, this gives us an iterative method for the solution of such matrix equations (e.g., Lyapunov's matrix equation where B = - A(T)), and on the other hand, the problem of choosing appropriate parameters for the block SOR method can be written in a more compact form which may be helpful, especially, for non-self-adjoint problems, i.e., if A and B are nonsymmetric. Using this technique, we determine-under more general assumptions than those of Chin and Manteuffel-the optimal SOR parameters for the model problem of a convection-diffusion equation.