On the use of relaxation parameters in hybrid smoothers

Abstract The use of relaxation parameters in hybrid smoothers within algebraic multigrid (AMG) is analysed both theoretically and practically. Relaxation parameters that are optimal under the assumptions of the theory are determined. The implementation of a procedure to automatically determine outer relaxation parameters for symmetric positive definite smoothers is described. Numerical results are presented, which show significant improvements over AMG with undamped hybrid smoothers. Copyright © 2004 John Wiley & Sons, Ltd.