Algebraic multigrid methods (AMG) for solving large systems of linear equations, Ax=b, are matrix-based analogs of geometric multigrid methods. Both types of methods are multi-level, and at each level utilize a smoothing procedure which is applied to residual vectors, and a coarse grid computation which is designed to reduce smoothed residual errors.

In this paper we consider AMG procedures which are based upon papers of Ruge and Stüben and present a simple modification for accelerating the convergence of such procedures. We also illustrate interesting phenomena which are important in studying the convergence of multigrid procedures, including significant differences in convergence rate which may be obtained using different choices of starting configurations.