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Line 13: ==Explanation of the method== We use the three preceding iterates, ''x''<sub>''n''-−2</sub>, ''x''<sub>''n''-−1</sub> and ''x''<sub>''n''</sub>, with their function values, ''f''<sub>''n''-−2</sub>, ''f''<sub>''n''-−1</sub> and ''f''<sub>''n''</sub>. Applying the [[Lagrange polynomial\|Lagrange interpolation formula]] to do quadratic interpolation on the inverse of ''f'' yields :<math> f^{-1}(y) = \frac{(y-f_{n-1})(y-f_n)}{(f_{n-2}-f_{n-1})(f_{n-2}-f_n)} x_{n-2} + \frac{(y-f_{n-2})(y-f_n)}{(f_{n-1}-f_{n-2})(f_{n-1}-f_n)} x_{n-1} </math> Line 23: ==Behaviour== The asymptotic behaviour is very good: generally, the iterates ''x''<sub>''n''</sub> 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 ''f''<sub>''n''-−2</sub>, ''f''<sub>''n''-−1</sub> and ''f''<sub>''n''</sub> coincide, the algorithm fails completely. Thus, inverse quadratic interpolation is seldomly used as a stand-alone algorithm. ==Comparison with other root-finding methods==

Inverse quadratic interpolation: Difference between revisions