Behaviour
The asymptotic behaviour is very good: generally, the iterates xn converge fast to the root once they get close. However, performance is often quite poor if you do not start very close to the actual root. For instance, if by any chance two of the function values fn−2, fn−1 and fn coincide, the algorithm fails completely. Thus, inverse quadratic interpolation is seldom used as a stand-alone algorithm.
The order of this convergence is approximately 1.8, it can be proved by the Secant Method analysis.
Read more about this topic: Inverse Quadratic Interpolation
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