Translator Disclaimer
2019 Nonstationary interpolatory subdivision schemes reproducing high-order exponential polynomials
Jie Zhou, Hongchan Zheng, Zhaohong Li, Weijie Song
Rocky Mountain J. Math. 49(7): 2429-2457 (2019). DOI: 10.1216/RMJ-2019-49-7-2429

Abstract

We present a family of nonstationary interpolatory subdivision schemes which reproduces high-order exponential polynomials. First, by extending the classical $\fbox {D-D}$ interpolatory schemes, we present the explicit expression of the symbols that identify a family of the nonstationary interpolatory subdivision schemes. These schemes can allow reproduction of more exponential polynomials, and represent exactly circular shapes, parts of conics which are important analytical shapes in geometric modeling. Furthermore, a rigorous analysis regarding the smoothness of the new nonstationary interpolatory schemes is provided. Next, based on the recursive formulas of the symbols, a repeated local operation is proposed for rapidly computing new points from the old points. Finally, two examples are presented to illustrate the performance of the new schemes.

Citation

Download Citation

Jie Zhou. Hongchan Zheng. Zhaohong Li. Weijie Song. "Nonstationary interpolatory subdivision schemes reproducing high-order exponential polynomials." Rocky Mountain J. Math. 49 (7) 2429 - 2457, 2019. https://doi.org/10.1216/RMJ-2019-49-7-2429

Information

Published: 2019
First available in Project Euclid: 8 December 2019

zbMATH: 07152872
MathSciNet: MR4039977
Digital Object Identifier: 10.1216/RMJ-2019-49-7-2429

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

JOURNAL ARTICLE
29 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.49 • No. 7 • 2019
Back to Top