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TW 310
J. Simoens and S. Vandewalle
Average-interpolating wavelet bases on irregular meshes on the interval
Abstract
The stabilized two-step construction of wavelet bases is applied to the one-dimensional case of irregular meshes on the interval. The method yields biorthogonal bases in which the wavelets on both the primal and the dual side have a chosen number of vanishing moments and have local support. The primal scaling functions are average-interpolating by construction. Uniform L2-stability is shown under a mild restriction on the irregularity of the mesh. Numerical results show that the wavelet bases are well-conditioned, having approximately the same condition numbers as wavelet bases obtained by full semiorthogonalization, while the average support is only slightly larger than in the unstabilized construction.
report.pdf / mailto: J. Simoens