Author(s): Liu, Zhongyun ; Yang, Jian ; Xu, Xiaofei ; Lin, Mengzhu ; Zhang, Yulin
Date: 2025
Persistent ID: https://hdl.handle.net/1822/93726
Origin: RepositóriUM - Universidade do Minho
Subject(s): Curve interpolations; Cubic B-spline basis; WGS-PIA algorithm; Optimal weight; Convergence
The weighted Gauss-Seidel-progressive iterative approximation (WGS-PIA) algorithm for cubic B-spline curve interpolations is considered in this paper. The convergence of the WGS-PIA algorithm is analyzed, and an upper bound whichis strictly smaller than one for the contraction factor of this WGS-PIA algorithm is derived. It is shown that for cubic B-spline curve interpolations, the GS-PIA algorithm converges faster than the Jacobi-PIA (J-PIA) algorithm, and that there always exists a positive weight ω such that the WGS-PIA converges faster than GS-PIA. Particularly, we derive a formula for the effective weight ω⋆ and the “theoretically optimal” weight ωm, which significantly improves the performance of the WGS-PIA algorithm with minimal additional cost. The numerical experiments are shown that for a given termination tolerance, the number of iterations and the CPU time required by the WGS-PIA algorithm are less than those required by the GS-PIA algorithm.
