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Question: convergence of the Newton iterative method

Question:convergence of the Newton iterative method

Lonely 400 Maple
May 27 2009
0

 

Hi,

we know that:

X(n+1) =Xn - f(x_n)/f^\prime(x_n)

Now I am using the following commands for showing the 2nd order convergence of the above method:

> restart;
> f(a) :=0: 
> A := taylor(f(x), x = a, 4);
>
> B := taylor((D(f))(x), x = a, 4);
> C := series(e[n]-A/(D(f))(x), x = a, 3);
> simplify(subs(x-a = e[n], %));
 

it does not cancel e_n

I know there must be a better way of doint it. Can you please tell me?

 

 
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