# Thread: Newton's Method: Numerical Analysis

1. ## Newton's Method: Numerical Analysis

Could someone please so me how Newton's Method is used in Numerical Analysis? My teacher is doing a horrible job of teaching it and he skips a lot of steps.

Newtons Method:

X(n+1) = x(n) - f(x(n))/f'(x(n)) (n) is a subcript to x.

2. Originally Posted by Dream
Could someone please so me how Newton's Method is used in Numerical Analysis? My teacher is doing a horrible job of teaching it and he skips a lot of steps.

Newtons Method:

X(n+1) = x(n) - f(x(n))/f'(x(n)) (n) is a subcript to x.
It is a method to find the solutions to a function using the derivative and the original function only

For example consider $\displaystyle x^4-3x^3+17\sin(x)=0$

We have to make an initial guess..lets say 2

So we set up our first iteration

$\displaystyle x_1=2-\frac{(2)^4-3(2)^4+17\sin(2)}{4(2)^2-9(2)^2+17\cos(2)}=\psi$

C is just because I dont have my calculator

So then

$\displaystyle x_2=\psi-\frac{\psi^4-3\psi^4+17\sin(\psi))}{4\psi^3-9\psi^2+17\cos(\psi)}$

and then obviously

$\displaystyle x_n=\psi_n-\frac{\psi_n^4-3\psi_n^3+17\sin(\psi_n)}{4\psi_n^3-9\psi_n^2+17\cos(\psi_n)}$

and as $\displaystyle n\to\infty$ the iterations will yield that zero of th function

3. Thanks guys. Newton's Method seems to be very simple to understand. It just was my teacher, who cann't really teach but he knows his stuff. Mainly I see that you can manipulate problems in many ways to get your desired outcome.