Hierarchical method for elliptic problems using wavelet

Zhiqiang Cai, E. Weinan

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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 languageEnglish (US)
Pages (from-to)819-825
Number of pages7
JournalCommunications in Applied Numerical Methods
Issue number11
StatePublished - 1992

All Science Journal Classification (ASJC) codes

  • General Engineering


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