Minimum Quadratic Error

$$\boxed{{\mathbf{a}}_{\min }={\left(A^{\top }A\right)}^{-1}{A}^{\top }\mathbf{y}}$$

with $J\left({\mathbf{a}}_{\min }\right)={\min }_{a\in {\mathbb{R}}^M}J(\mathbf{a})$ where,

• $\mathbf{a}\to$Weights
• $A\to$Ansatz points
• $\mathbf{y}\to$Given dependent variables