If the fixed-point iteration is applied to the function F(x) = 2 + (x-2)^4, starting at x = 2.5, what order of convergence results? Find the range of starting values for which this fixed-point iteration converges. Note that 2 is a fixed point.
Please provide as much detail as possible so that I can understand how the solution is derived. I would like to understand this problem so that I can apply the techniques used to similar problems. I really appreciate your help!© BrainMass Inc. brainmass.com October 10, 2019, 1:42 am ad1c9bdddf
Assume that is the root of the fixed point equation
In addition is continuously differentiable for all x near and for some .
Furthermore, assume that
Then if the initial guess is sufficiently close to , the iteration
Fixed-point iterations are analyzed.