Given a root-finding function f(x)=0, what is the sufficient global/local convergence condition of inverse quadratic interpolation?
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In Brent's original 1971 paper that had introduced this method, also in his book Algorithms for Minimization without Derivatives, he mentioned the local convergence condition is that $f$ has a Lipschitz continuous derivative near the root we would like to find.
For the global convergence, Brent didn't gave the requirement for global convergence or something similar in the book. And in the notes here, the author gives the a universal global convergence condition, see Theorem 5.1 Sharkovsky’s No-Swap Theorem. (PS. the pdf isn't properly rendered in Google Chrome web browser)