Wavelet-Galerkin Methods
Using wavelets as basis for the test and trial spaces of a Galerkin method allows an optimal preconditioning of the stiffness matrix. It is proven that a diagonal scaling provides such a preconditioning. In order to avoid to compute and store the non-sparse wavelet stiffness matrix one uses the Fast Wavelet Transform. Several numerical comparisons are provided.
Keywords: Wavelet preconditioning, Fast Wavelet Transform, Diagonal preconditioning
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