Another area if concern of the minimization problem is the slow convergence rate. It becomes particularly serious when the size of the problem is large. Different acceleration methods, such as multigrid method and the hierarchical basis method [3], [5], have been proposed to speed up the convergence.
Both the multigrid method and the hierarchical basis methods employ the multiresolution concept in improving the convergence rate. Another way is to use wavelet transform techniques [8], [6].
In [6], the orthogonal wavelet transform uses two sets of bases, i.e., the wavelets and the scaling functions, with larger support to replace the original basis. The consequence of such a basis transfer is a preconditioning of the associated equation system. It results in significant improvement in the convergence rate. However, the issue of discontinuities is not addressed.
In [8], orthogonal wavelets are used as a preconditioning transform. The discrete wavelet transform is directly applied to diagonalize the linear equation system of the discretized interpolation problem. With this diagonal preconditioning, a fast solution with fewer iterations is obtained by approximating the off-diagonal terms of the preconditioned equation system to be zero. The discontinuities are found separately using the bending moment approach as in [3].