  The convergence rate of a multigrid method depends on the properties of the
smoother and the so-called grid transfer operator. In this paper we define and
analyze new grid transfer operators with a generic cutting size which are
applicable for high order problems. We enlarge the class of available geometric
grid transfer operators by relating the symbol analysis of the coarse grid
correction with the approximation properties of univariate subdivision schemes.
We show that the polynomial generation property and stability of a subdivision
scheme are crucial for convergence and optimality of the corresponding
multigrid method. We construct a new class of grid transfer operators from
primal binary and ternary pseudo-spline symbols. Our numerical results
illustrate the behavior of the new grid transfer operators.
