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Math Help - Fixed Point Iteration

  1. #1
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    Fixed Point Iteration

    I'm having problems finding a good way to simplify F(x)=0 in the form of x=
    Its there a Tip or trick to find it faster. I'm posting some examples

    F(x)=x^3-1.33x^2+x-1.33
    Not converges  x= -x^3 +1.33x^2 +1.33
    it converges x=(1.33*(x^2+1)-x)^1/3

    what about this one g(x) = e^3 - tan(x)
    How can I Rewrite g(x)=0 as another fixed-point equation, that actually let find a suitiable fixed point.

    Cheers,
    Alexis
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  2. #2
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    Quote Originally Posted by aleba008 View Post
    I'm having problems finding a good way to simplify F(x)=0 in the form of x=
    Its there a Tip or trick to find it faster. I'm posting some examples

    F(x)=x^3-1.33x^2+x-1.33
    Not converges  x= -x^3 +1.33x^2 +1.33
    it converges x=(1.33*(x^2+1)-x)^1/3

    what about this one g(x) = e^3 - tan(x)
    How can I Rewrite g(x)=0 as another fixed-point equation, that actually let find a suitable fixed point.
    You could write g(x)=0 as \sin x = e^3\cos x or \cos x = e^{-3}\sin x, leading to x = \arcsin(e^3\cos x) or x= \arccos(e^{-3}\sin x). The first of those does not look promising, but the second one converges very rapidly from the starting point x_0 = \pi/2.
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