The extended block Arnoldi method for solving generalized differential Sylvester equations

In the present paper, we propose a new method for solving large-scale generalized differential Sylvester equations, by projecting the initial problem onto the extended block Krylov subspace with an orthogonality Galerkin condition. This projection gives rise to a low-dimensional generalized differential Sylvester matrix equation. The low-dimensional equations is then solved by Rosenbrock or BDF method. We give some theoretical results and report some numerical experiments to show the effectiveness of the proposed method.

Keywords:

Extended block Krylov subspace , Generalized differential Sylvester matrix equation , low-rank approximate solution , Rosenbrock method , BDF method