Multigrid methods for variation problems: The V-cycle

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In an earlier paper, we developed a convergence theory for a class of multigrid methods applied to differential boundary value problems, where the differential operator is self-adjoint and positive definite. The multigrid structure assumed a variational setting (although it applies to finite differences as well as finite elements) and incorporated the so-called W-cycle process. In the present paper, we extend this theory to include some results on the corresponding V-cycle multigrid algorithm.