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An efficient convergence test for the fixed point method

mohamedlamine's picture

The fixed point method consists to find the solution of F(X)=X.

One can not get fixed with the convergence condition |F'(X)|<1 because if the function has an optimum then |F'(X)|=0 even if the solution is not yet reached.

 

We introduce an efficient convergence test with the condition:

|Xn+1 - Xn| ≤ epsilon1 And |F(Xn+1)-Xn+1| ≤ epsilon2

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