CONVERGENCE-ESTIMATES FOR MULTIGRID ALGORITHMS

To estimate convergence of the multigrid algorithms, we need some assu mptions on smoothers. The assumptions for typical smoothers are well a nalyzed in the multigrid literature [1,2]. However, numerical evidence shows that Kaczmarz smoother does not satisfy above assumptions. Thus , we introduce a weaker condition which is satisfied by Kaczmarz smoot her as well as Jacobi and Gauss-Seidel smoother. Under these weaker as sumptions, we show that the convergence factor of V-cycle multigrid al gorithm is delta = 1-1/(C(j-1)). These assumptions for Kaczmarz smooth er are verified by numerical experiment.