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arXiv · 1410.2729

Convergence of univariate non-stationary subdivision schemes via asymptotical similarity

Costanza Conti·Nira Dyn·Carla Manni·Marie-Laurence Mazure
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Abstract

A new equivalence notion between non-stationary subdivision schemes, termed asymptotical similarity, which is weaker than asymptotical equivalence, is introduced and studied. It is known that asymptotical equivalence between a non-stationary subdivision scheme and a convergent stationary scheme guarantees the convergence of the non-stationary scheme. We show that for non-stationary schemes reproducing constants, the condition of asymptotical equivalence can be relaxed to asymptotical similarity. This result applies to a wide class of non-stationary schemes of importance in theory and applications.

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Costanza Conti, Nira Dyn, Carla Manni, Marie-Laurence Mazure. 2014-10-10. Convergence of univariate non-stationary subdivision schemes via asymptotical similarity. https://arxiv.org/abs/1410.2729

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