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

Document Type : Research Article


ENSA Oujda, Equipe MSN, Lab. LM2N, Université Mohammed Premier, Oujda, Morocco


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.


Main Subjects