Convergence analysis of a multi-level relaxation method

We analyse a multi-level method based on successive projections of descent directions into vector spaces os smaller dimensions than the original space. We first show that the original space can be splitted into a direct sum (in the sense of the energy norm) of n+1 orthogonal spaces where n is the number of levels. Using this result, we then show that the convergence properties of this method are identical to the convergence properties of more classical multigrid methods.