Connection coefficients of interval wavelets satisfying boundary conditions

Abstract

The computation of connection coefficients is an important issue in the wavelet numerical solution of partial differential equations. We study this problem for the orthonormal interval wavelets bases, satisfying homogeneous boundary conditions, introduced by Monasse and Perrier. We first obtain explicit expressions to compute the connection coefficients involving (derivatives of) scaling functions at the same level. Then we describe how to compute connection coefficients when we have (derivatives of) scaling functions and/or wavelets at different levels, using local refinement relations.