Krylov subspace restart scheme for solving large-scale Sylvester equations

The development of efficient interior point methods has greatly enlarged the range of control problems with feasible numerical solution. These methods are nevertheless difficult to solve for large-scale problems. In this paper we suggest the use of a Krylov subspace technique for the efficient low-rank approximate solution to large-scale Sylvester equations. The suggested method is a novel restart scheme which improves further the computation efficiency and storage requirements of the standard Krylov subspace methods for the solution of large-scale Sylvester equations.