Convergence of multivariate non-stationary vector subdivision schemes

Authors:
Maria Charina;Costanza Conti
Affiliations:
Institut für Angewandte Mathematik, Universität Dortmund, 44221 Dortmund, Germany;Dipartimento di Energetica "Sergio Stecco", Università di Firenze, Via Lombroso 6/17, 50134 Firenze, Italy
Venue:
Applied Numerical Mathematics - Special issue: Applied scientific computing - Grid generation, approximated solutions and visualization
Year:
2004

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Abstract

Any non-stationary subdivision scheme is associated with masks that may vary from one scale to the next finer one. In this paper we investigate the convergence of non-stationary vector subdivision schemes in Zd. In particular, we present a strategy for deriving non-stationary difference subdivision schemes whose zero convergence guarantee the convergence of the original schemes. This strategy is similar to the one presented in [C. Conti, M. Charina, Regularity of multivariate vector subdivision schemes, in preparation], where the convergence and the regularity of stationary multivariate vector subdivision schemes is analyzed.