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Thread: Fixed point iteration

  1. #1
    Bar0n janvdl's Avatar
    Apr 2007

    Fixed point iteration

    Hey guys,

    I'm struggling a bit with this problem. Just confused I guess.

    The equation $\displaystyle f(x) = e^x - 3x^2 = 0$ has 3 roots. To determine the roots by fixed point iteration we can rearrange the equation to obtain the iteration formulas: $\displaystyle x = g(x) = \pm \sqrt{\frac{e^x}{3}}$
    Determine analytically the largest interval $\displaystyle [a,b]$, so that for any $\displaystyle p_0 \ \text{element of} \ [a,b]$ the iteration formula with the minus sign will converge to a root close to -0.5. You must therefore find the largest interval on which the conditions of the Fixed Point theorem are satisfied.
    I've drawn the graphs (see attached), and $\displaystyle g(x)$ approaches 0 as x approaches negative infinity. But it doesn't make sense to me that the interval can be [-inf, b] where b is the rightmost bound of the interval.

    I'm just very confused I guess. Can I get a push in the right direction?
    Attached Thumbnails Attached Thumbnails Fixed point iteration-mhf.png  
    Last edited by janvdl; Feb 2nd 2010 at 07:49 AM.
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