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Advances in Computational Mathematics

, Volume 45, Issue 3, pp 1273–1290 | Cite as

A new computable sufficient condition for the convergence of subdivision schemes with nonnegative masks

  • Li ChengEmail author
  • Xinlong Zhou
Article
  • 46 Downloads

Abstract

We are interested in nontrivial conditions on the nonnegative masks that guarantee the convergence of the correspondent subdivision schemes. Roughly speaking, a certain convexity of the support of the given mask implies the convergence of the subdivision scheme. Moreover, those conditions are computable. The key of proving our main theorem is to find out an irreducible or primitive mapping on some multi-integer set and to show the uniqueness of this mapping.

Keywords

Convergence Nonnegative mask Additive mapping Subdivision scheme 

Mathematics Subject Classification (2010)

65D17 26A18 39B12 

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Notes

Acknowledgements

The authors are indebted to the referees for various helpful comments on their paper.

Funding information

The first author is supported partly by the National Natural Science Foundation of China No. 11701246 and Science and Technology Planning Project of Lishui City, China (2014RC21).

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics and Institute of Nonlinear AnalysisLishui UniversityLishuiChina
  2. 2.Faculty of MathematicsUniversity of Duisburg-EssenDuisburgGermany

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