地图投影的最小二乘二元多项式拟合的误差估计

探讨了在地图投影的最小二乘二元多项式拟合中参考点的分布对拟合误差的影响,提出了一种基于矩阵的秩亏的方法来判断参考点是否在指定次数的二元多项式空间的代数曲线上,并导出在极小范数最小二乘意义下的拟合多项式的误差估计式,公式表明拟合误差和参考点的最小二乘误差无关。

Error estimate of the least squares binary polynomial fitting for map projection

This paper discusses the impact that the distribution of reference points has on the error of least squares binary polynomial fitting for map projection, and puts forward a method based on the rank of some matrix to judge whether these reference points lay on the algebra curve in the space spanned by the binary polynomial with certain order. Then derive the expressions of the error estimate under the condition of the minimal norm and the least squares binary polynomial fitting. The expressions indicate that the error of the least squares on these reference points isn't related to the fitting error.