最佳拟合直线的理论分析及快速逼近算法

The Analysis and Fast Approximating Algorithm of Best Fitting Line

本文用Chbeshev逼近理论对美国标准ISA-537.1中所定义最佳直线的存在性、唯一性及充要条件进行了严格的理论分析。给出了判别最佳拟合直线的几何判别准则。在此基础上,根据最佳拟合直线的特征构造了一种快速逼近算法。计算结果表明,与最小二乘直线和K-L最佳拟合直线相比,用快速逼近算法计算得出的最佳拟合直线线性度最好。

In this paper the theory of Chebeshev approximation is used to strictly and theoretically analyze the existence, uniquness and necessury and sufficient condition of the best fitting line defined in Amarican standand ISA—537. 1. According to the characteristic theorem of the best fitting line, a new fast approximating algorithm is presented. The linearity computed by the fast approximating algorithm is better than by least square and K-L best fitting line.