# Newton's Method

• Nov 29th 2008, 06:30 PM
Fosite
Newton's Method
Apply newton's method to the equation $\displaystyle x^2-a=0$ to derive the following square-root algorithm: $\displaystyle Xn+1= \frac12(Xn+a/Xn)$

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

What's next?...
• Nov 30th 2008, 02:40 PM
Fosite
Come on guys... I really need help (Wondering)
• Nov 30th 2008, 02:51 PM
TheEmptySet
Quote:

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

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

What's next?...

Just plug into the formula for Newtons method

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

and simplify and whola you are done :)
• Nov 30th 2008, 04:37 PM
Fosite
Quote:

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

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

and simplify and whola you are done :)

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