On the generalized ADI method for the matrix equation X−AXB=C

The paper investigates a rational approximation problem in connection with the convergence analysis of the ADI iterative method applied to the matrix equation X−AXB=C. In the real case, a complete theory on the characterization and unicity of the optimal solution as well as on the convergence of a Remes like algorithm for its computation, is presented. Numerical experiments provide some comparison with asymptotically optimal solutions which have been previously reported, particularly in applications for image restoration.