In this paper, we concern with the data interpolation by using extended cubic uniform B-splines with shape parameters. Two iterative formats, namely the progressive iterative approximation (PIA) and the weighted progressive iterative approximation (WPIA), are proposed to interpolate given data points. We study the optimal shape parameter and the optimal weight for the proposed methods by solving the eigenvalues of the collocation matrix. The optimal shape parameter can make the iterative methods not only have the fastest convergence speed but also have smallest initial interpolation error. Numerical experiments are given to illustrate the effectiveness of the proposed methods.

在本文中，我们通过使用带有形状参数的扩展三次均匀B样条来进行数据插值。提出了两种迭代格式，即渐进式迭代逼近（PIA）和加权渐进式迭代逼近（WPIA），以内插给定的数据点。我们通过求解搭配矩阵的特征值来研究所提出方法的最佳形状参数和最佳权重。最优的形状参数可以使迭代方法不仅收敛速度最快，而且初始插值误差最小。数值实验说明了所提方法的有效性。