Inverse quadratic interpolation: Difference between revisions

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Line 26: 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 the initial values are not 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 seldom used as a stand-alone algorithm. The order of this convergence is approximately 1.84 as can be proved by [[~~Secant~~secant ~~Method~~method]] analysis. ==Comparison with other root-finding methods== Line 40: ==References== *[[James F. Epperson]], [https://books.google.com/books?id=Mp8-z5mHptcC&pg=PA182 An introduction to numerical methods and analysis], pages ~~182-185~~182–185, Wiley-Interscience, 2007. {{isbn\|978-0-470-04963-1}} {{root-finding algorithms}} [[Category:Root-finding algorithms]]