Semi-algebraic Multi-level Methods Based on Wavelet Decompositions I: Application to Two-point Boundary Value Problems

To clarify more precisely the vague but often indicated connection between wavelet and multi-grid theory is the main goal of the article. Therefore we present a multi-level method based on a wavelet approximation of the succesive error of a classical iterative solver. The resulting iteration is a hybrid between a purely algebraic multi-level technique and the usual multi-grid technique related to a discretization of an elliptic diierential operator. It shows the typical multi-grid convergence behaviour, even if it is not able to compete at this stage with the eecient multi-grid iterations. Nevertheless, our new approach has the capacity to solve linear equations arising from the discretization of integral operators of the rst kind by multi-level techniques.