Block linear method for large scale Sylvester equations

We present and analyze a new iterative scheme for large-scale solution of the well-known Sylvester equation. The proposed scheme is based on fixed point iteration approach and can make good use of the recently developed methods for solving block linear systems. It is shown mathematically that the iterative process converges under some assumptions on the coefficient matrices. Results on our numerical experiments with large-scale matrices are quite encouraging. In particular, the method compares favorably with the other block methods and a recently proposed method for Sylvester equation based on low-rank approximation of the right hand side matrix C.