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Mathematics of Computation

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Subsequence convergence in subdivision

Author: Deter de Wet
Journal: Math. Comp. 80 (2011), 973-994
MSC (2010): Primary 65D10, 65D17, 41A99
Published electronically: October 18, 2010
MathSciNet review: 2772104
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Abstract: We study the phenomenon that regularly spaced subsequences of the control points in subdivision may converge to scalar multiples of the same limit function, even though subdivision itself is divergent. We present different sets of easily checkable sufficient conditions for this phenomenon (which we term subsequence convergence) to occur, study the basic properties of subsequence convergence, show how certain results from subdivision carry over to this case, show an application for decorative effects, and use our results to build nested sets of refinement masks, which provide some insight into the structure of the set of refinable functions. All our results are formulated for a general integer dilation factor.

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Deter de Wet
Affiliation: Department of Mathematical Sciences, Mathematics Division, Private Bag X1, Matieland 7602, South Africa

Received by editor(s): April 16, 2008
Received by editor(s) in revised form: April 29, 2009
Published electronically: October 18, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.