Preconditioned geometric iterative methods for B-spline interpolation

Chengzhi Liu, Yue Qiu and Li Zhang

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 219, issue C, 87-100

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.

Keywords: Geometric iterative method; Progressive iterative approximation; Preconditioning technique; Data interpolation; Cubic B-spline (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:219:y:2024:i:c:p:87-100

DOI: 10.1016/j.matcom.2023.12.010

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