Adaptive Wavelet‐Frame Method with Stable Boundary Adapted Bases
Dana Černá, Václav Finěk · AIP conference proceedings · 2008
The compression property of wavelets led to design of adaptive wavelet methods for solving operator equations. The effectiveness of these methods is strongly influenced by the choice of the used wavelet basis, in particular by the condition of these bases. In our contribution, we propose a construction of spline‐wavelet bases on the interval adapted to complementary boundary conditions of the first order. The resulting bases are well‐conditioned and the corresponding stiffness matrices have small condition numbers. Furthermore, we show that the adaptive wavelet frame method from [8] with bases constructed in our contribution realizes the optimal convergence rate.