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Preconditioned progressive iterative approximation for tensor product Bézier patches

Author

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  • Liu, Chengzhi
  • Liu, Zhongyun
  • Han, Xuli

Abstract

Based on the diagonally compensated reduction, the preconditioned progressive iterative approximation (PPIA) for tensor product Bézier patches is presented. Due to the effectiveness of the preconditioner, the convergence rate of progressive iterative approximation (PIA) is accelerated significantly. To improve the robustness and reduce the computational complexity of PPIA, the inexact PPIA format for tensor product Bézier patches is presented. Several numerical examples are presented to illustrate the effectiveness of the proposed methods.

Suggested Citation

  • Liu, Chengzhi & Liu, Zhongyun & Han, Xuli, 2021. "Preconditioned progressive iterative approximation for tensor product Bézier patches," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 372-383.
    • Handle: RePEc:eee:matcom:v:185:y:2021:i:c:p:372-383
    DOI: 10.1016/j.matcom.2021.01.002
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    References listed on IDEAS

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    1. Izquierdo, Diego & de Silanes, María Cruz López & Parra, María Cruz & Torrens, Juan José, 2014. "CS-RBF interpolation of surfaces with vertical faults from scattered data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 102(C), pages 11-23.
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    Cited by:

    1. Liu, Chengzhi & Qiu, Yue & Zhang, Li, 2024. "Preconditioned geometric iterative methods for B-spline interpolation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 87-100.
    2. Zhuang, Jiayuan & Zhu, Yuanpeng & Zhong, Jian, 2024. "Curve fitting by GLSPIA," Applied Mathematics and Computation, Elsevier, vol. 466(C).

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