Solution of the Sylvester equation on a parallel computer

This paper is concerned with a parallel solution of the Sylvester matrix equation AX+XB=C by means of the iterative method of successive approximations. In this work convergence conditions for the method are given. If the matrices A and B have a block partitioned form, different choices of the splittings of A and B are presented. In this case at each iteration of the method, one has to solve a set of independent Sylvester equations, which can be solved in parallel by means of a direct method. By using the multisplitting principle it has been also introduced an explicit parallelism in the method. The implementation of the iterative method on a distributed memory system such as Cray T3D has been described and the results of some computational experiments related to the solution of the Riccati equation, have been presented