Numerical analysis problem

Discussion in 'Math' started by tedeman, Feb 15, 2009.

  1. tedeman

    Thread Starter New Member

    May 12, 2008
    2
    0
    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
     
  2. studiot

    AAC Fanatic!

    Nov 9, 2007
    5,005
    513
    The condition for a fixed point is g(p) =p

    By substitution if p =1/A

    g(1/A) = 2/A - A(1/A^2) = 1/A(2 - 1) = 1/A

    as required.
     
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