Least squres(最小二乘法)

Least Squares Approximations

When $Ax=b$ has no solutions , multiply by $A^T$ and solve $A^{T}A\hat{x}=A^{T}b$ , $\hat{x}$ is least squares solution

例子：找一条最接近三个点（0，6），（1，0），（2，0）直线
如果存在一条直线 b=C+Dt 经过三个点，那么：
$$\begin{gathered} C+D\ast 0=6 \\ C+D\ast 1=0 \\ C+D\ast 2=0 \end{gathered}$$
写成矩阵形式：
[ 1 0 1 1 1 2 ] [ C D ] = [ 6 0 0