We study scalar multivariate non-stationary subdivision schemes with a general integer 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.
Reproduction of exponential polynomials by multivariate non-stationary subdivision schemes with a general dilation matrix / Maria Charina; Costanza Conti ; Lucia Romani. - In: NUMERISCHE MATHEMATIK. - ISSN 0029-599X. - STAMPA. - 127:(2014), pp. 223-254. [10.1007/s00211-013-0587-8]
Reproduction of exponential polynomials by multivariate non-stationary subdivision schemes with a general dilation matrix
CONTI, COSTANZA;
2014
Abstract
We study scalar multivariate non-stationary subdivision schemes with a general integer 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.File | Dimensione | Formato | |
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