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- #1

- Apr 13, 2013

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I have a question.

Given the equation $t(x)=x^{2}-3x-4=0$ which roots are $-1$ and $4$ , we are looking for a suitable iterative method $x_{n+1}=\varphi(x_{n}),n=0,1,2$ so that the sequence $(x_{n})$ converges to the root $4 \forall x_{0} \in [3,5] $.Which of the following would you choose?

1) $\varphi(x)=3+\frac{4}{x}$

2) $\varphi(x)=\frac{(x^2-4)}{3}$

3) $\varphi(x)=x^2-2x-4$

4) $\varphi(x)=\frac{(x^3-3x^2)}{4}$

How can I check which of the above is a suitable iterative method?