can anyone show me...

How do you prove that an iterative method is convergent??

like for example if you have $\displaystyle x_n = x_{n-1} - f(x_{n-1})/f'(x_{n-1})$

thank you (Rofl)

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- Mar 15th 2009, 09:55 PMpandakrapconvergence
can anyone show me...

How do you prove that an iterative method is convergent??

like for example if you have $\displaystyle x_n = x_{n-1} - f(x_{n-1})/f'(x_{n-1})$

thank you (Rofl) - Mar 16th 2009, 12:42 PMCaptainBlack
Well this is Newtom-Raphson and its convergence depends on where you start and what h(x) actually is. See the Wikipedia article.

CB - Mar 23rd 2009, 08:22 AMHallsofIvy
You can't. It isn't always. Whether it converges of not depends on the function f, the set of possible values of f (obviously, if $\displaystyle f(x)= x^2+ 1$ where x is required to be real, this will not converge since it must converge to a solution of f(x)= 0 and $\displaystyle x^2+ 1= 0$ doesn't have a real solution) and, even when f is such that it

**can**converge, whether it will or not depends on the initial choice of $\displaystyle x_0$.