New approaches for solving large Sylvester equations

In this paper, we propose two new algorithms based on modified global Arnoldi algorithm for solving large Sylvester matrix equations AX + XB = C where A∈Rn×n, B∈Rs×s, X and C∈Rn×s. These algorithms are based on the global FOM and GMRES algorithms and we call them by Global FOM-Sylvester-Like (GFSL) and Global GMRES-Sylvester-Like (GGSL) algorithms, respectively. Some theoretical results and numerical examples are also given.