Convergence estimates for multigrid algorithms (Q1376695)

The rate of convergence of multigrid algorithms is known to depend on assumptions concerning the smoothing process. The authors give a condition on smoothing that grants the optimal convergence of the multigrid method and is weaker than that considered by \textit{J. H. Bramble} and \textit{J. E. Pasciak} [Math. Comput. 58, No. 198, 467-488 (1992; Zbl 0771.65082)]. The new condition is shown to be satisfied also by the Kaczmarz smoother, unlike the conditions analyzed by Bramble and Pasciak [loc. cit.]. The importance of the new results is illustrated by numerical experiments.