基于相对误差的曲线最小二乘拟合

分析了最小二乘法的研究历史与现状,给出了高斯最小二乘法的几种研究思路,但是这些研究方法都没有考虑到高斯最小二乘法本身的缺陷。将通过一个实际的算例来分析高斯最小二乘法的缺陷基于绝对误差大体相同的前提之下,否则会产生很大的误差。在绝对误差相差不多的情况下,较小的数据的有可能产生较大的相对误差,这显然与实际情况不符。但通常情况下,观测数据往往按被观测量的相对误差进行评价,也就是说,被观测量越大,允许的实际观测量的误差也越大。从这个角度出发,将给出改进的最小二乘法。同时,从理论上证明其对应的法方程组的解是存在且唯一。最后给出相应的仿真算例,与高斯最小二乘法作比较,得到较好的结论。

Relative error based curve fitting for least square method

This paper analyses least square method in the research history and current situation,it has given several research ideas for the Gauss least squares method,but these methods do not consider defects of Gauss least square method.Through a practical example analysis of Gauss least square method of defect-based on the absolute error with same premise,otherwise it will result in great errors.In the absolute error of the same cases,smaller data is likely to produce a larger relative error,which is obviously inconsistent with the actual situation.But in normal circumstances,often in accordance with observed variable of relative error to evaluate observation data,that is to say,the observational data is larger;allow the actual measurement error is larger.From this perspective,we will suggest an improved least square method.At the same time,we proved theoretically the method to the solution of the equations is existent and unique.Finally,the emulated example is given,and Gauss least square method for comparison,it gets a better conclusion.