Abstract

Based on the Hermitian and skew-Hermitian splitting iteration technique, a new progressive iteration approximation technique called HPIA for curves and surfaces interpolation with normalized totally positive (NTP) bases and its weighted version, namely WHPIA, are proposed. We take the previous iteration and the current iteration into account simultaneously, and establish a function based on NTP bases as a perturbation term in the iteration process. Convergence analyses and the approximate optimal weight of WHPIA are given. Theoretical and experimental results show that HPIA and WHPIA are effective.

中文翻译：

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基于HSS迭代的基于NTP的曲线和曲面的迭代插值

摘要

基于Hermitian和skew-Hermitian分裂迭代技术，提出了一种新的渐进迭代逼近技术，称为HPIA，用于曲线和曲面插补，具有标准化的完全正（NTP）基及其加权版本，即WHPIA。我们同时考虑先前的迭代和当前的迭代，并在迭代过程中建立基于NTP基作为扰动项的函数。给出了收敛性分析和WHPIA的近似最佳权重。理论和实验结果表明，HPIA和WHPIA是有效的。