【摘要】 为了得到收敛速度更快的几何迭代法,提出带形状参数的三次均匀B样条扩展曲线的(加权)渐进迭代逼近法.首先基于三次均匀B样条扩展曲线提出(加权)渐进迭代逼近法的迭代格式;然后通过分析迭代矩阵的谱半径,探讨迭代法的最优形状参数及加权渐进迭代逼近法的最优权系数;最后指出双三次均匀B样条扩展曲面同样具有(加权)渐进迭代逼近性质.数值实例结果表明,所求的最优形状参数及权系数使得迭代法具有最快的收敛速度.更多还原

【Abstract】 In order to obtain faster convergence rate, we proposed the(weighted) progressive-iterative approximation by the extension of the cubic uniform B-spline curves with shape parameters. Firstly, we presented the(weighted) progressive-iterative approximation expression, and then studied the optimal shape parameters and the optimal weight by analyzing the spectral radius of the iterative matrix of the progressive-iterative approximation. Finally, we also proposed the(weighted) progressive-iterative approximation by the extension of bicubic uniform B-spline surfaces, and pointed out that the initial surface also has the(weighted) progressive iteration approximation property. Numerical results show that the optimal shape parameters and the optimal weight make the iterative methods have the fastest convergence rate.更多还原