Wavelet representation for multigrid computation in surface interpolation problem

Abstract

Discrete formulation of the surface interpolation problem usually leads to a large sparse linear system. The convergence rate for solving this problem with iterative method is very slow. To improve this condition, wavelet representation for multigrid computation is proposed. With wavelet transforms, the linear system to be solved will be transformed into a new system equation. This new system processes the low frequency and high frequency components more directly and more efficiently. By employing the multigrid computation structure among these different frequency components, a multi-frequency band computation structure which combines the advantages of the wavelet transform and the multigrid method is built. This structure not only avoids the transfer between the adjacent grids and results in a simple structure for implementation but also manipulates the different frequency components more effectively and results in a higher convergence rate for solving linear equation system.