(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

given [tex] f \in C^2 [/tex] such that [tex] f(a)=f'(a)=0 ^f''(a)\neq 0 [/tex] prove that the modified newton method [tex] x_{n+1}=x_n-2 \frac{f(x_n){f'(x_n)} [/tex] coverges with order two.

2. Relevant equations

if g(x) is an iterative function such that the first m derivatives of g at a are zero and [tex]g^{(m+1)}\neq 0 [/tex] then the order of convergence is m+2

3. The attempt at a solution

So it seems that i want to show that my iterating function [tex] g(x)=x-2 \frac{f(x){f'(x)} [/tex] satisfies [tex] g(a)=0 ^ g'(a)\neq 0 [/tex]

But using le'hospitals rule to find g(a) i have [tex] g(a)=a-2\frac{f'(a)}{f''(a)}=a \neq 0 [/tex]

Whats wrong here?

Thanks

Tal

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# Accelerated newton method

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