This is what Griewank et al. call "Piecewise linearization in secant mode", see for instance https://opus4.kobv.de/opus4-zib/files/6164/newton_secant_approx_paper.pdf. The aim of that research was to capture the kinks of absolute value operations with the same precision a tangent or a secant captures the local behavior of a smooth function, with an ...


Potentially related and useful (I gave these resources to my students when teaching Intro to Computational Mathematics, kinda useful pedagogically too): "Automatic Source-to-Source Error Compensation of Floating-Point Programs" by Laurent Thévenoux, Philippe Langlois and Matthieu Martel : https://hal.archives-ouvertes.fr/hal-01158399/document ...


Define the iteration $$ x_{n+1} = f(x_n) $$ Then $$ e_n := \frac{\|x_{n+1} - x_n\|}{\| x_n - x_{n-1}\|} \le L $$ Compute $e_n$ and that should tell you something about L. If the iterations converge ($L < 1$), then $e_n$ should converge to $L$.

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