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Stationary binary subdivision schemes using radial basis function interpolation

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Abstract

A new family of interpolatory stationary subdivision schemes is introduced by using radial basis function interpolation. This work extends earlier studies on interpolatory stationary subdivision schemes in two aspects. First, it provides a wider class of interpolatory schemes; each 2L-point interpolatory scheme has the freedom of choosing a degree (say, m) of polynomial reproducing. Depending on the combination (2L,m), the proposed scheme suggests different subdivision rules. Second, the scheme turns out to be a 2L-point interpolatory scheme with a tension parameter. The conditions for convergence and smoothness are also studied.

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Authors and Affiliations

  1. Division of Internet Engineering, Dongseo University, Busan, 617-716, S. Korea

    Byung-Gook Lee

  2. Department of Mathematics and Institute for Mathematical Sciences, Ewha W. University, Seoul, 120-750, S. Korea

    Yeon Ju Lee & Jungho Yoon

Authors
  1. Byung-Gook Lee
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  2. Yeon Ju Lee
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  3. Jungho Yoon
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Additional information

Communicated by R. Schaback

Dedicated to Prof. Charles A. Micchelli on the occasion of his 60th birthday

Mathematics subject classifications (2000)

41A05, 41A25, 41A30, 65D10, 65D17.

Byung-Gook Lee: This work was done as a part of Information & Communication fundamental Technology Research Program supported by Ministry of the Information & Communication in Republic of Korea.

Jungho Yoon: Corresponding author. Supported by the Korea Science and Engineering Foundation grant (KOSEF R06-2002-012-01001).

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Lee, BG., Lee, Y.J. & Yoon, J. Stationary binary subdivision schemes using radial basis function interpolation. Adv Comput Math 25, 57–72 (2006). https://doi.org/10.1007/s10444-004-7642-z

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  • DOI: https://doi.org/10.1007/s10444-004-7642-z

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