New Smoothing Iterative Block Methods for Linear Systems with Multiple Right-hand Sides

Abstract

In the present paper, we propose new smoothing procedures for iterative block methods for solving nonsymmetric linear systems of equations with multiple right-hand sides. These procedures generalize those known for solving linear systems with one right-hand. We first give some properties of these new algorithms. Then new methods such as the global minimal residual smoothing (GMRS) algorithm and the smoothed global biconjugate gradient (SGL-BCG) algorithm are introduced. Finally, numerical examples are given.