# Newton's Method

• November 29th 2008, 07:30 PM
Fosite
Newton's Method
Apply newton's method to the equation $x^2-a=0$ to derive the following square-root algorithm: $Xn+1= \frac12(Xn+a/Xn)$

$f(x)=x^2-a$
$f'(x)=2x$

What's next?...
• November 30th 2008, 03:40 PM
Fosite
Come on guys... I really need help (Wondering)
• November 30th 2008, 03:51 PM
TheEmptySet
Quote:

Originally Posted by Fosite
Apply newton's method to the equation $x^2-a=0$ to derive the following square-root algorithm: $Xn+1= \frac12(Xn+a/Xn)$

$f(x)=x^2-a$
$f'(x)=2x$

What's next?...

Just plug into the formula for Newtons method

$x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}$

and simplify and whola you are done :)
• November 30th 2008, 05:37 PM
Fosite
Quote:

Originally Posted by TheEmptySet
Just plug into the formula for Newtons method

$x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}$

and simplify and whola you are done :)

my question is which X1 should I choose? and is the final formula always contains $a$?