Newton's Method: Numerical Analysis

**Dream** · June 8th 2008, 06:31 PM

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.

**Mathstud28** · June 8th 2008, 07:38 PM

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 $x^4-3x^3+17\sin(x)=0$

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

So we set up our first iteration

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

C is just because I dont have my calculator

So then

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

and then obviously

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

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

**arbolis** · June 12th 2008, 01:10 PM

Check out http://online.math.uh.edu/HoustonACT...ewton-H264.mov.

**Dream** · June 12th 2008, 01:33 PM

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.

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