bug#58929: 29.0.50; Calc: finding roots utpn doesn't work as advertised

[Eli Zaretskii]

> Cc: 58929@debbugs.gnu.org
> From: Mattias Engdegård <mattiase@acm.org>
> Date: Thu, 3 Nov 2022 09:53:02 +0100
> 
> Of course an actual numerical analyst would know immediately what to do. Is 
> there one in the audience?

I have good experience from using this technique:

  
https://www.researchgate.net/publication/226830173_On_the_Structure_of_Zero_Finders

It employs a hybrid method that doesn't need derivatives (but is
almost as fast as Newton).  However, its main advantage (which is a
huge one in some real-life situations) is that the structure of the
algorithm allows the caller to make arbitrary modifications to the
approximations that the algorithm produces, and in general have
complete control on the iterations' process.  In particular, one can
easily deal with situations where the root approximation goes out of
the expected range, or lands in the area where the function doesn't
behave well enough.