This directory contains the mask matrices of the biorthogonal multigenerators and wavelets on the interval as constructed in W. Dahmen, B. Han, R.-Q. Jia, A. Kunoth, Biorthogonal Multiwavelets on the Interval: Cubic Hermite Splines, (4.8 MB) Constr. Approx. 16, 2000, 221-259. All the following explanations refer to this article. (Mathematical symbols are written using latex-commands.)
We provide here the decomposition and reconstruction matrices M_j and G_j for the minimal level j=j_0=3. The matrices can be found in sparse matlab format in the Matlab files
The matrices defined in the Matlab files are denoted by Mj and Gj. One can check that Gj is the inverse of Mj. The matrix Mj is divided as written in Corollary 5.2 into two matrices M_{j,0} and M_{j,1} which have the structure (4.4.7). Correspondingly, Gj consists of two block matrices G_{j,0} and G_{j,1}, see Corollary 5.2. Recall that these transformation matrices perform decomposition and reconstruction between two levels. For more levels, one assembles M_j and G_j for each level, noting that the corner blocks of the matrices due to the boundary adaptation always remain the same and only the interior blocks grow.
Last modified: 21.12.2009