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Preconditioned geometric iterative methods for B-spline interpolation

Author

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  • Liu, Chengzhi
  • Qiu, Yue
  • Zhang, Li

Abstract

The geometric iterative method (GIM) is widely used in data interpolation/fitting, but its slow convergence affects the computational efficiency. Recently, much work has been done to guarantee the acceleration of GIM in the literature. This work aims to accelerate the convergence rate by introducing a preconditioning technique. After constructing the preconditioner, we preprocess the progressive iterative approximation (PIA) and its variants, called the preconditioned GIMs. We show that the proposed preconditioned GIMs converge, and the extra computation cost of the preconditioning technique is negligible. Several numerical experiments are given to demonstrate that our preconditioner can accelerate the convergence rate of PIA and its variants.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:219:y:2024:i:c:p:87-100
    DOI: 10.1016/j.matcom.2023.12.010
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    References listed on IDEAS

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    1. Huahao Shou & Liangchen Hu & Shiaofen Fang, 2022. "Progressive Iterative Approximation of Non-Uniform Cubic B-Spline Curves and Surfaces via Successive Over-Relaxation Iteration," Mathematics, MDPI, vol. 10(20), pages 1-17, October.
    2. 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.
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