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Calculation method

  1. Sep 7, 2005 #1
    Hi,
    in the method -Theory of Fixed Point Iteration of x = g(x)

    If the function g(x) has several roots, why sometimes we need to change the form of g(x) to find the other roots?

    For example we can have x3+3x2+x+4,
    one form can be x= -x3-3x2-4
    or
    another form can be
    x=sqrt(-x3-3x2-4) / sqrt (3)

    those two forms converge into diffrent values.WHY?

    Thank you

    Brad
     
  2. jcsd
  3. Sep 7, 2005 #2
    You've misunderstood the whole thing!

    Definition: A fixed point of a function g(x) is a number p such that p = g(p).

    Caution. A fixed point is not a root of the equation 0 = g(x), it is a solution of the equation x = g(x).

    Geometrically, the fixed points of a function g(x) are the point(s) of intersection of the curve y = g(x) and the line y = x.
     
  4. Sep 7, 2005 #3
    Ok that makes more sense now.

    Thank you very much
     
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