University of GuilanJournal of Mathematical Modeling2345-394X12120240301An improved extended block Arnoldi method for solving low-rank Lyapunov equation8598731810.22124/jmm.2023.25670.2281ENIliasAbdaouiENSA Oujda, Equipe MSN, Lab. LM2N, Université Mohammed Premier, Oujda, MoroccoJournal Article20230928We 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.https://jmm.guilan.ac.ir/article_7318_dff6b430202ad958d6708c49eeebba7f.pdf