Based on the diagonally compensated reduction, the preconditioned progressive iterative approximation (PPIA) for tensor product Bézier patches is presented. Due to the effectiveness of the preconditioner, the convergence rate of progressive iterative approximation (PIA) is accelerated significantly. To improve the robustness and reduce the computational complexity of PPIA, the inexact PPIA format for tensor product Bézier patches is presented. Several numerical examples are presented to illustrate the effectiveness of the proposed methods.

中文翻译：

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张量积贝塞尔补丁的预处理渐进式迭代逼近

基于对角线补偿的减少量，提出了张量积贝塞尔补丁的预处理渐进迭代逼近（PPIA）。由于预处理器的有效性，渐进式迭代逼近（PIA）的收敛速度大大提高。为了提高PPIA的鲁棒性并降低其计算复杂性，提出了张量积Bézier补丁的不精确PPIA格式。几个数值例子被提出来说明所提出的方法的有效性。