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A New Method for the Analysis of Univariate Nonuniform Subdivision Schemes

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Abstract

This paper presents a new method for the analysis of convergence and smoothness of univariate nonuniform subdivision schemes. The analysis involves ideas from the theory of asymptotically equivalent subdivision schemes and nonuniform Laurent polynomial representation together with a new perturbation result. Application of the new method is presented for the analysis of interpolatory subdivision schemes based upon extended Chebyshev systems and for a class of smoothly varying schemes.

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Acknowledgments

This work was supported by Basic Science Research Program 2012R1A1A2004518 and Priority Research Centers Program 2009-0093827 through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology

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Authors and Affiliations

  1. School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel-Aviv University, Ramat-Aviv, 69978 , Tel-Aviv, Israel

    Nira Dyn & David Levin

  2. Department of Mathematics, Ewha Womans University, Seoul , 120-750, South Korea

    Jungho Yoon

Authors
  1. Nira Dyn
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  2. David Levin
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  3. Jungho Yoon
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Correspondence to David Levin.

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Communicated by Peter Oswald.

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Dyn, N., Levin, D. & Yoon, J. A New Method for the Analysis of Univariate Nonuniform Subdivision Schemes. Constr Approx 40, 173–188 (2014). https://doi.org/10.1007/s00365-014-9247-1

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  • DOI: https://doi.org/10.1007/s00365-014-9247-1

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