I am having trouble picking a good initial value for a fixed point iteration method that I am running. The trouble is, the function is not always the same. Depending on the input of the user, the function could be x = 1/(f(x^20)) or x = 1 / (f(x^50)), and a very complicated function that that. It usually converges picking the simple value of 2, but sometimes it does not. Does anybody know how I could go about writing a program to help me select the initial point to guaruntee convergence? Thanks.