HP calcs are really not that accurate..

[AlexFekken]

(12-04-2017 09:05 AM)ttw Wrote:  One must use the "Interval Newton Method" which isn't Newton's method converted to interval arithmetic (as I described above).

https://ww2.ii.uj.edu.pl/~zgliczyn/cap07/krawczyk.pdf

That's a bit disappointing.

Looking at your first reference (the pdf), the requirements on f ensure that is is injective. In the one-dimensional situation this implies (together with smoothness) that it must be strictly monotonic. This is very restrictive and even the simple example f(x)=x^3-2x+2 does not meet the requirement.