Characterization of some convergent bivariate subdivision schemes with nonnegative masks

摘要

Knowing that the convergence of a multivariate subdivision scheme with a nonnegative mask can be characterized by whether or not some finite products of row-stochastic matrices induced by this mask have a positive column. However, the number of those products is exponential with respect to the size of matrices. For nonnegative univariate subdivision, this problem is completely solved. Thus, the convergence in this case can be checked in linear time with respect to the size of a square matrix. This paper will demonstrate the necessary and sufficient conditions for the convergence of some nonnegative bivariate subdivision schemes by means of the so-called connectivity of a square matrix, which is derived by a given mask. Moreover, the connectivity can be examined in linear time with respect to the size of this matrix. (C) 2019 Elsevier Inc. All rights reserved.