February 2024 ANISOTROPIC SUBDIVISION WITH THE OPTIMAL REPRODUCTION PROPERTY
Baoxing Zhang, Hongchan Zheng, Yingwei Chen, Meng Li
Rocky Mountain J. Math. 54(1): 319-329 (February 2024). DOI: 10.1216/rmj.2024.54.319

Abstract

This paper presents several families of anisotropic interpolatory subdivisions satisfying the optimal reproduction property with the dilation matrix diag(3,2). Such schemes are obtained based on the discussion of the relationship between sum rules and polynomial generation for anisotropic schemes. The corresponding masks are symmetric about the origin and imply that, with a relaxed requirement on symmetry, different families of similar schemes with the optimal reproduction property can be obtained. We also show that, given the unimodular matrices Θ,Θ, the interpolatory schemes with the dilation matrix Θdiag(3,2)Θ and the ones with the dilation matrix diag(3,2) have the same reproduction property. The convergence of these new schemes is analyzed based on the convergence analysis in the isotropic case. Some numerical examples are given to illustrate the performance of these new schemes.

Citation

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Baoxing Zhang. Hongchan Zheng. Yingwei Chen. Meng Li. "ANISOTROPIC SUBDIVISION WITH THE OPTIMAL REPRODUCTION PROPERTY." Rocky Mountain J. Math. 54 (1) 319 - 329, February 2024. https://doi.org/10.1216/rmj.2024.54.319

Information

Received: 1 August 2022; Accepted: 19 December 2022; Published: February 2024
First available in Project Euclid: 28 February 2024

MathSciNet: MR4718522
Digital Object Identifier: 10.1216/rmj.2024.54.319

Subjects:
Primary: 65D05 , 65D17 , 68U05

Keywords: anisotropic dilation matrix , interpolatory subdivision , multiple subdivision , optimal reproduction property , sum rules

Rights: Copyright © 2024 Rocky Mountain Mathematics Consortium

Vol.54 • No. 1 • February 2024
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