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

Abstract

In \u00a0the \u00a0present \u00a0paper, \u00a0we \u00a0propose \u00a0new \u00a0smoothing \u00a0procedures \u00a0for \u00a0iterative \u00a0block \u00a0methods \u00a0for solving \u00a0nonsymmetric \u00a0linear \u00a0systems \u00a0of \u00a0equations \u00a0with \u00a0multiple \u00a0right-hand \u00a0sides. \u00a0These \u00a0procedures 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.