最小二乘多项式拟合

对于给定数据点若使用多项式进行拟合，即：
$$\phi (x)=a_0+a_{1}x+...+a_n{x}^n$$
则最小二乘的法方程组为
$$\left[\begin{array}{cccc}m& \sum x_i& \cdots & \sum x_i^n\\ \sum x_i& \sum x_i^2& \cdots & \sum x_i^{n+1}\\ ⋮& ⋮& \ddots & ⋮\\ \sum x_i^n& \sum x_i^{n+1}& \cdots & \sum x_i^{2n}\end{array}\right]\left[\begin{array}{c}{a}_0\\ a_1\\ ⋮\\ a_n\end{array}\right]=\left[\begin{array}{c}\sum y_i\\ \sum x_i{y}_i\\ ⋮\\ \sum x_i^n{y}_i\end{array}\right]$$