Originally Posted by

**Twig** Hi

Not really sure where to post this question, but here we go.

I need to compute the first several iterations of Newtonīs method for solving

$\displaystyle x^{2}-1=0 $ , using initial guess $\displaystyle x_{0}=10^{6} $ .

First things first. How would this be set up?

$\displaystyle \mbox{Newtons method: }x_{k+1}=x_{k} - \frac{f(x_{k})}{f'(x_{k})} $

Would this give me:

$\displaystyle x_{1}=10^{6}-\frac{(10^{6})^{2}-1}{2\cdot 10^{6}} $

If so, how do I decide in general the apparent convergence rate?

What should the asymptotic convergence rate be?

How many iterations are required before the asymptotic convergence is reached?

Finally, give an analytical explanation of the behavior one observes.

I donīt even know what asymptotic convergence is.

Thanks!