Newton's method, the full name of Newton's method.
When N = 1,
The basic idea of Newton's method is: for f (x) do second-order Taylor expansion in the vicinity of the estimated value of the existing minimum point, and then find the next estimate of the minimum point. Set 
the estimated present value of the minimum point, then through a second-order Taylor:
Because it is seeking the most value, and 
should meet
which is
Obtained
So 
, then
When N> 1, more than two dimensions. Second-order Taylor expansion can be done to promote.
For the gradient vector of f 
is f the Hessian matrix, defined as follows.
make
Similarly,
then
If the non-singular matrix, the presence of the inverse matrix, which can be solved as follows:
Newton method algorithm pseudo-code:
1) Given the initial values x0 and precision threshold ε, and let k: = 0
2) Calculation 
and
3) If 
, then stop the iteration, otherwise determine the search direction
4) Calculate the new iteration point,
5) Order
6) Go 2
Disadvantages: original Newton iteration formula in the law does not step factor, given 
iteration, for non-quadratic objective function, and sometimes will function values rise, indicating that Newton's law can not guarantee the function value steadily decline, in severe cases, even It may result in an iterative sequence of points 
failed diverge.