Theory of Fixed Point Iteration of x = g(x)
Fixed point iteration is a method for finding roots of an equation
f(x) = 0 if it can be cast into the form
x = g(x).
Given an initial guess x0 we can compute the
iteration sequence
x0 , x1 , x2 , ...
defined by
xn = g(xn-1), for n = 1, 2, 3, ...
If this sequence converges to the number r then r = g(r) so r is a
root of x = g(x). However, in many cases the sequence doex not converge.
Even if it converges the convergence rate may be slow.
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