Hierarchical method for elliptic problems using wavelet
Zhiqiang Cai, E Weinan · Communications in Applied Numerical Methods · 1992
Abstract 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(log 2 H / h ) in two dimensions, and the condition number of the wavelet preconditioning system is bounded by O(log 2 H / h ) in d dimensions, instead of O( h −2 ) if the scaling function bases are used.