An improved extended block Arnoldi method for solving low-rank Lyapunov equation

We are interested in the numerical solution of the continuous-time Lyapunov equation. Generally, classical Krylov subspace methods for solving matrix equations use the Petrov-Galerkin condition to obtain projected equations from the original ones. The projected problems involves the restrictions of the coefficient matrices to a Krylov subspace. Alternatively, we propose a scheme based on the extended block Krylov subspace that leads to a smaller-scale equation, which also incorporates  the restriction of the inverse of the Lyapunov equation s square coefficient. The effectiveness of this approach is experimentally confirmed, particularly in terms of the required CPU time.