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Thread: Fixed point iteration

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    Bar0n janvdl's Avatar
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    Meh
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    Fixed point iteration

    Hey guys,

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

    Background:
    The equation 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: x = g(x) = \pm \sqrt{\frac{e^x}{3}}
    Question:
    Determine analytically the largest interval [a,b], so that for any 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 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 08:49 AM.
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