Newton'o metodai

Metodas Newton'o, kai

$$\begin{eqnarray}s_n=H_n^{-1} grad\ f(x^n), \end{eqnarray}$$

kur Hessian'as

$$\begin{eqnarray}H_n=(\frac{\partial^2 f(x^n)}{\partial x_i \ \partial x_j},\ i,j=1,...,m). \end{eqnarray}$$

Metodas kvazi-Newton'o, kai

$$\begin{eqnarray}H_n^{-1} \approx G_n, \end{eqnarray}$$

kur

$$\begin{eqnarray}G_{n+1}=G_n -\frac{(G_n \gamma_n)(G_n \gamma_n)^T }{\gamma_n^T G_n \gamma_n}+ \frac{\delta_n\ \delta_n^T}{\delta_n^T\ \gamma_n}. \end{eqnarray}$$

Cia $T$ transponavimo zenklas,

$$\begin{eqnarray}\gamma_n =grad\ f(x_n)-grad\ f(x_{n-1}),\\ \delta_n=x^n-x^{n-1},\\ G_0=I. \end{eqnarray}$$