We study the effect of interpolation and restriction operators on the convergence of multigrid algorithms for
solving linear PDEs. Using a modal analysis of a subclass of these systems, we determine how two groups of
the modal components of the error are filtered and mixed at each step in the algorithm. We then show that the
convergence rate of the algorithm depends on both the properties of the interpolation and restriction operators
and the characteristics of the system. The analysis opens the problem of optimization of these operators. By
different choices of operators we show a trade-off between the optimization of the convergence rate and the
optimization of the number of computations required per iteration.
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