Estimating the joint spectral radius of a nonseparable multiwavelet

The joint spectral radius p of 2 matrices is related to the boundedness of all their products. Calculating p is known to be NP-hard. In this work, we estimate the joint spectral radius associated to a bidimensional separable multiwavelet, in order to analyze its Holder continuity. To the author´s knowledge this has not been done. The analysis aims at testing the applicability of the multiwavelet transform to those aspects of image processing where continuous basis functions perform best, such as image synthesis, image magnification and image compression. We adapt an algorithm due to Heil and Colella, that works for unidimensional wavelets, to our more complex setting, to prove that p < 1, and show the performance of the multiwavelet for image magnification.