Stationary binary subdivision schemes using radial basis function interpolation

Byung Gook Lee; Yeon Ju Lee; Jungho Yoon

doi:10.1007/s10444-004-7642-z

Stationary binary subdivision schemes using radial basis function interpolation

Byung Gook Lee, Yeon Ju Lee, Jungho Yoon

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

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.

Original language	English
Pages (from-to)	57-72
Number of pages	16
Journal	Advances in Computational Mathematics
Volume	25
Issue number	1-3
DOIs	https://doi.org/10.1007/s10444-004-7642-z
State	Published - Jul 2006

Bibliographical note

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

Keywords

Multiquadrics
Radial basis function interpolation
Subdivision scheme

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10.1007/s10444-004-7642-z

Cite this

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N2 - 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.

AB - 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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JF - Advances in Computational Mathematics

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ER -

Stationary binary subdivision schemes using radial basis function interpolation

Abstract

Bibliographical note

Keywords

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