On the effective construction of compactly supported wavelets satisfying homogeneous boundary conditions on the interval

Abstract

We construct compactly supported wavelet bases satisfying homogeneous boundary conditions on the interval [0, 1]. The maximum features of multiresolution analysis on the line are retained, including polynomial approximation and tree algorithms. The case of H10([0, 1]) is detailed and numerical values, required for the implementation, are provided for the Neumann and Dirichlet boundary conditions. © 1997 Academic Press.