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Thread: numerical analisys question..

  1. #1
    MHF Contributor
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    numerical analisys question..

    http://i48.tinypic.com/2yzd213.jpg

    how they got g1 g2 g3
    ?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by transgalactic View Post
    http://i48.tinypic.com/2yzd213.jpg

    how they got g1 g2 g3
    ?
    They are just different rearrangemants of $\displaystyle x^3-x-5=0$ into the form $\displaystyle x=g(x)$, presumably to show that formula iteration converges for some but not others.

    $\displaystyle g_1(x)$ comes from the rearrangement $\displaystyle x=x^3-5$

    $\displaystyle g_2(x)$ comes from the rearrangement $\displaystyle x^3=x-5$, so $\displaystyle x= \sqrt[3]{x-5}$

    $\displaystyle g_3(x)$ comes from the rearrangement $\displaystyle x(x^2-1)-5=0$ so $\displaystyle x=\frac{5}{x^2-1}$

    CB
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  3. #3
    MHF Contributor
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    ok i solved a similar equation:
    $\displaystyle x^3+2x^2+4-x=0$
    $\displaystyle g1=x^3+2x^2+4$

    why for g1 L=0.5
    how to find L for other g
    what is the meaning of L?
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