Bounds for smoothness of refinable functions Original Research Article

The Villemoes machine can be used to compute the Sobolev smoothness of a refinable function. We start with presenting this technique. It involves the computation of the spectral radius of a special matrix which has at least quadratic time complexity with respect to the refinement mask size. For the one-dimensional case we deduce by linear algebra some simple estimates which require only a few basic operations on the mask coefficients with a total of linear time complexity. For orthogonal Daubechies and biorthogonal CDF wavelet generators the estimates are compared to the known regularities.