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Concerning Order of Convergence for Subdivision

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Abstract

We discuss order of convergence for subdivision algorithms, in the scalar-valued and the vector-valued case. In order to find the generic order, the usual definition of convergence order is extended, refering to a proper quasi interpolant operator whose representation on polynomial spaces can be constructively determined with recourse to properties of the subdivision mask. Assuming stability and smoothness of the limit functions, the approximation order of the quasi interpolant operator determines the order of convergence of subdivision.

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Authors and Affiliations

  1. Dipartimento di Energetica, Università di Firenze, Via C. Lombroso 6/17, I-50134, Firenze, Italy

    C. Conti

  2. Institut für Angewandte Mathematik und Statistik, Universität Hohenheim, D-70593, Stuttgart, Germany

    K. Jetter

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  1. C. Conti
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Conti, C., Jetter, K. Concerning Order of Convergence for Subdivision. Numer Algor 36, 345–363 (2004). https://doi.org/10.1007/s11075-004-3896-2

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