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Math Help - Picking good initial value for fixed point iteration

  1. #1
    JDW
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    Picking good initial value for fixed point iteration

    Hi,

    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.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by JDW View Post
    Hi,

    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.
    You need a condition derived from the Banach fixed point theorem.

    CB
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