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Math Help - Numerical analysis problem

  1. #1
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    Numerical analysis problem

    Let A be a given positive constant and g(x)=2x-Ax^2

    a. Show that if fixed-point iteration converges to a nonzero limit, then the
    limit is p=1/A, so the reciprocal of a number can be found using only
    multiplications and subtractions
    b. Find an interval about 1/A for which fixed-point iteration converges,
    provided p0 is in the interval

    Can any one help with this problem
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by tedeman View Post
    Let A be a given positive constant and g(x)=2x-Ax^2

    a. Show that if fixed-point iteration converges to a nonzero limit, then the
    limit is p=1/A, so the reciprocal of a number can be found using only
    multiplications and subtractions
    b. Find an interval about 1/A for which fixed-point iteration converges,
    provided p0 is in the interval

    Can any one help with this problem
    if the iteration x_{n+1}=g(x_n) converges then it convergent to a root of:

    g(x)=x

    For the second part you need to find an interval about 1/A such that g'(x)<k<1 on that interval, then the contraction mapping (Banach's fixed point) theorem will guarantee convergence.

    CB
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