Convergence analysis of multigrid methods with residual scaling techniques
Journal of Computational and Applied Mathematics
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We consider multigrid methods for symmetric positive definite linear systems. We present a new algebraic convergence analysis of two-grid schemes with inexact solution of the coarse grid system. This analysis allows us to bound the convergence factor of such perturbed two-grid schemes, assuming only a certain bound on the convergence factor for the unperturbed scheme (with exact solution of the coarse grid system). Applied to multigrid methods with the standard W-cycle, this analysis shows that if the convergence factor of the (unperturbed) two-grid method is uniformly bounded by $\sigma