On some extended block Krylov based methods for large scale nonsymmetric Stein matrix equations

Abstract

In the present paper, we consider the large scale Stein matrix equation with a low-rank constant term AXB - X + EFT = 0. These matrix equations appear in many applications in discrete-time control problems, filtering and image restoration and others. The proposed methods are based on projection onto the extended block Krylov subspace with a Galerkin approach (GA) or with the minimization of the norm of the residual. We give some results on the residual and error norms and report some numerical experiments.