A note on convergence of the multigrid V-cycle

摘要

Several recent papers have discussed the convergence of the multigrid V-cycle. In particular there are several results for the symmetric case: where the numbers of smoothings before the fine-to-coarse transfer and after the coarse-to-fine transfer are the same. In most instances, the smoother H=I−E-1A has been limited to the case where E is positive definite and the eigenvalues h of H satisfy 0⩽h⩽1. In this note we extend these results to asymmetric V-cycles and the case where -b⩽h⩽1 with 0