改进的局部多项式插值权函数研究

基于动态球半径选点法选取构建多项式的样本点，分别采用局部距离比、反距离权重及本文所引进的选权迭代法3种方法，对局部多项式插值结果的准确度与可靠性进行对比分析。结果表明，在无粗差情况下，3种定权方法插值结果相似；而加入粗差后，前2种方法的结果偏离无粗差情况下的插值曲面，而选权迭代法得到的曲面起伏情况与无粗差结果一致。

Study on Improved Local Polynomial Interpolation Weight Function

Abstract: We select the sample points of the construction polynomial based on the dynamic circle radius selection method, and select three weight functions, including the local distance ratio, the inverse distance weighted, and weighted iteration method. We compare and analyze the accuracy and reliability of the local polynomial interpolation results. It is shown that the results of three methods are similar without gross error. When the gross error is added, the results of the first two methods deviate from the interpolated surface without gross error, and the undulation of weighted iteration method is consistent with previous result.