Methods of Curve Fitting ■ Suppose that we are given the points (),(x2),...,(x)and want to fit an exponential curve of the form y=Ce x The coefficients 4 and C should be determined. The nonlinear least-squares procedure requires that we find a minimum of E(A,C)=N=(CeAxk-yk)2.We set the partial derivatives of E(4,C)to zero and then simplified,the resulting normal equations are ce2-立e=0 -∑ye=0 k=1Methods of Curve Fitting ◼ Suppose that we are given the points (x1 ,y1 ),(x2 ,y2 ),…,(xN,yN) and want to fit an exponential curve of the form y=CeAx . ◼ The coefficients A and C should be determined. ◼ The nonlinear least-squares procedure requires that we find a minimum of 𝐸 𝐴, 𝐶 = σ𝑘=1 𝑁 (𝐶𝑒 𝐴𝑥𝑘 − 𝑦𝑘) 2 . We set the partial derivatives of E(A, C) to zero and then simplified, the resulting normal equations are 2 1 1 2 1 1 0 0 k k k k N N Ax Ax k k k k k N N Ax Ax k k k C x e x y e C e y e = = = = − = − =    