Multivariate Re nement Equations and Subdivision Schemesx
نویسنده
چکیده
Reenement equations play an important role in computer graphics and wavelet analysis. In this paper we investigate multivariate reenement equations associated with a dila-tion matrix and a nitely supported reenement mask. We characterize the L p-convergence of a subdivision scheme in terms of the p-norm joint spectral radius of a collection of matrices associated with the reenement mask. In particular, the 2-norm joint spectral radius can be easily computed by calculating the eigenvalues of a certain linear operator on a nite-dimensional linear space. Examples are provided to illustrate the general theory.
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