Low rank approximate solutions to large Sylvester matrix equations

In the present paper, we propose an Arnoldi-based method for solving large and sparse Sylvester matrix equations with low rank right hand sides. We will show how to extract low-rank approximations via a matrix Krylov subspace method. We give some theoretical results such an expression of the exact solution and upper bounds for the norm of the error and for the residual. Numerical experiments will also be given to show the effectiveness of the proposed method.