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.
Highlights
We are interested in the numerical solution of large scale nonsymmetric Stein matrix equations of the form: AXB − X + EF T = 0 (1)
Stein matrix equations play an important role in many problems in control and filtering theory for discrete-time large-scale dynamical systems, in each step of Newton’s method for discrete-time algebraic Riccati equations, model reduction problems, image restoration techniques and other problems [1,2,3,4,5,6,7,8,9,10]
We presented in this paper two iterative methods for computing numerical solutions for large scale Stein matrix equations with low rank right-hand sides
Summary
We are interested in the numerical solution of large scale nonsymmetric Stein matrix equations of the form: AXB − X + EF T = 0. To solve large linear matrix equations, several Krylov subspace projection methods have been proposed (see, e.g., [1,13,14,15,16,17,18,19,20,21,22,23,24] and the references therein). The main idea developed in these methods is to use a block Krylov subspace or an extended block Krylov subspace and project the original large matrix equation onto these Krylov subspaces using a Galerkin condition or a minimization property of the obtained residual.
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