Reproduction of Exponential Polynomials by Multivariate Non-stationary Subdivision Schemes with a General Dilation Matrix
Provides a theoretical tool for researchers working on subdivision schemes in geometric modeling and approximation theory.
The paper characterizes the reproduction of exponential polynomials by multivariate non-stationary subdivision schemes with a general dilation matrix, providing algebraic conditions on symbols for checking and constructing such schemes.
We study scalar multivariate non-stationary subdivision schemes with a general dilation matrix. We characterize the capability of such schemes to reproduce exponential polynomials in terms of simple algebraic conditions on their symbols. These algebraic conditions provide a useful theoretical tool for checking the reproduction properties of existing schemes and for constructing new schemes with desired reproduction capabilities and other enhanced properties. We illustrate our results with several examples.