最小二乘解与高斯消元法的注记

A Note on Least Squares Solutions and Gaussian Eliminations

若在对超定线性方程组求最小二乘解的过程中使用高斯消元法(即对增广的系数矩阵作初等行变换),有时会得到正确的最小二乘解,但大多数情况下是错误的.探讨了高斯消元法和最小二乘解的一些关系.建议授课时提醒学生注意最小二乘法和求解一般的线性方程组的区别.

If we use Gaussian eliminations(i.e.do elementary row operations on the augmented matrix)to find least squares solutions for overdetermined linear equations,sometimes we will obtain the correct solutions.However,in general it yields wrong answers.We discuss some relations between Gaussian eliminations and least squares solutions,intending to remind beginners to pay attention to their difference.