Progressive Iterative Approximation for Extended Cubic Uniform B-Splines with Shape Parameters

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.