There exist variants of Newton’s method with safeguards against non-convergence (escape bracket, not converging “fast enough”, etc, in which case they switch to a bracketing method like Brent’s or bisection). Various implementations I found differ in details, and I could not find a paper with conver…

References and implementation for safe/hybrid univariate Newton's method

j_verzani September 23, 2022, 3:18pm 14

I forget if the convergence analysis is in detail, but in the LithBoonkkampIJzermanBracket method of find_zero from Roots there is an implementation of this kind of algorithm and a reference to follow up on.

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References and implementation for safe/hybrid univariate Newton's method

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