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 A X B − X + E F T = 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.

Keywords

• extended block Krylov subspaces
• low-rank approximation
• Stein matrix equation
• Galerkin approach (GA)
• minimal residual (MR) methods