Global least squares method (Gl-LSQR) for solving general linear systems with several right-hand sides

In this paper, we propose a new method for solving general linear systems with several right-hand sides. This method is based on global least squares method and reduces the original matrix to the lower bidiagonal form. We derive a simple recurrence formula for generating the sequence of approximate solutions {Xk}. Some theoretical properties of the new method are discussed and we also show that how this method can be implemented for the sylvester equation. Finally, some numerical experiments on test matrices are presented to show the efficiency of the new method.