In this paper we explore the hierarchical structures of wavelets, and use them for solving the linear systems which arise in the discretization of the wavelet-Galerkin method for elliptic problems. It is proved that the condition number of the stiffness matrix with respect to the wavelet bases grows like O(log2 H/h) in two dimensions, and the condition number of the wavelet preconditioning system is bounded by O(log2 H/h) in d dimensions, instead of O(h-2) if the scaling function bases are used.
|Original language||English (US)|
|Number of pages||7|
|Journal||Communications in Applied Numerical Methods|
|State||Published - 1992|
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