All Newton methods are based on approximating the objective function
locally by a quadratic model and then minimizing that function
approximately. The quadratic model of the objective function **f**
at along is given by the expansion

The minimum of the right-hand side is achieved when is the minimum of the quadratic function:

Alternatively, such a * Newton direction*
satisfies the linear system of **n**
simultaneous equations, known as the * Newton equation*: