Minimal residual methods augmented with eigenvectors for solving Sylvester equations and generalized Sylvester equations

In this paper we propose minimal residual methods augmented with eigenvectors for solving large Sylvester matrix equations AX + XB = C and generalized Sylvester matrix equations AXB + X = C. The subspace, from which the approximate solution is extracted, is the Kronecker product subspace of two augmented Krylov subspaces. Numerical experiments report the effectiveness of these methods.