Convergence estimates for multigrid algorithms - Kang, K.S.; Kwak, D.Y. (Computers & mathematics with applications (1987), 1997)
To estimate convergence of the multigrid algorithms, we need some assumptions on smoothers. The assumptions for typical smoothers are well analyzed 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 smoother as well as Jacobi and Gauss-Seidel smoother. Under these weaker assumptions, we show that the convergence factor of V-cycle multigrid algorithm is δ = 1 − 1 (C(j − 1)) . assumptions for Kaczmarz smoother are verified by numerical experiment.