The convergence rate of a multigrid method depends on the properties of thesmoother and the so-called grid transfer operator. In this paper we define andanalyze new grid transfer operators with a generic cutting size which areapplicable for high order problems. We enlarge the class of available geometricgrid transfer operators by relating the symbol analysis of the coarse gridcorrection with the approximation properties of univariate subdivision schemes.We show that the polynomial generation property and stability of a subdivisionscheme are crucial for convergence and optimality of the correspondingmultigrid method. We construct a new class of grid transfer operators fromprimal binary and ternary pseudo-spline symbols. Our numerical resultsillustrate the behavior of the new grid transfer operators.
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