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Math Help - Contraction mapping iterations

  1. #1
    TS1
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    Contraction mapping iterations

    contraction mapping
    phi x=((x^2)-2x+5)/4 with phi restricted to [0,2]

    set up an iterative scheme with x0=1/2. give estimate on the maximum number of iterations needed to approach fixed point with error of less than 10^(-k) for any integer k??
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  2. #2
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    Quote Originally Posted by TS1 View Post
    contraction mapping
    phi x=((x^2)-2x+5)/4 with phi restricted to [0,2]

    set up an iterative scheme with x0=1/2. give estimate on the maximum number of iterations needed to approach fixed point with error of less than 10^(-k) for any integer k??
    A "fixed point" for phi is x such that \frac{x^2- 2x+ 5}{4}= x. That is the same as x^2- 2x+ 5= 4x or 6x= x^2+ 5 so  x= \frac{x^2+ 5}{6}. Try that as an "iterative scheme".
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