Fixed-point iteration
![The fixed-point iteration xn+1 = sin xn with initial value x0 = 2 converges to 0. This example does not satisfy the assumptions of the Banach fixed point theorem and so its speed of convergence is very slow.](/Images/godic/202501/13/Sine_fixed_point.svg3950.png")
In numerical analysis, fixed-point iteration is a method of computing fixed points of iterated functions.
More specifically, given a function ![f](/Images/godic/202501/13/8fa14cdd754f91cc6554c9e71929cce73950.png")
defined on the real numbers with real values and given a point ![x_0](/Images/godic/202501/13/0b21a666a81629962ade8afd967826ed3950.png")
in the domain of , the fixed point iteration is