A Stabilized Lifting Construction of Wavelets on Irregular Meshes on the Interval
Jo Simoens, Stefan Vandewalle · SIAM Journal on Scientific Computing · 2003
We propose a stabilization of the two-step lifting construction of Sweldens for wavelet bases on 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. We combine it with a constrained local semiorthogonalization to obtain a stabilized variant. Numerical results show that the wavelet bases are well-conditioned, having approximately the same condition numbers as wavelet bases obtained by global semiorthogonalization, while the average support is not much larger than in the unstabilized construction.