最小二乘法(Least Squares Fitting)

least squares fitting proceeds by finding the sum of the squares of the vertical deviationsR2of a set of n data points:
最小二乘法(Least Squares Fitting)
文章图片

The condition forR2to be a minimum is that
最小二乘法(Least Squares Fitting)
文章图片

for i=1, …, n. For a linear fit,
最小二乘法(Least Squares Fitting)
文章图片

so
最小二乘法(Least Squares Fitting)
文章图片

These lead to the equations
最小二乘法(Least Squares Fitting)
文章图片

In matrix form,
最小二乘法(Least Squares Fitting)
文章图片

so
最小二乘法(Least Squares Fitting)
文章图片

The 2×2 matrix inverse is
最小二乘法(Least Squares Fitting)
文章图片

so
最小二乘法(Least Squares Fitting)
文章图片

【最小二乘法(Least Squares Fitting)】原文链接:Least Squares Fitting

    推荐阅读