Mattias Engdegård <mattiase@acm.org> writes:

> Obviously the claim to guarantee a solution for "any initial guess" is
> fanciful.

Yes.  See attached patch for what I wish the docs had said all along
(would have saved me a lot of time).


> Unfortunately straight Newton won't converge for this function (erf,
> essentially) if you stray too far from the origin (ie, the mean) so I
> suggest you always use that as a starting guess no matter what point
> you are trying to find the inverse for.
>
> Another way is to use an interval as starting guess instead of a
> single point; that seems to make Calc switch tactics and persevere.

I wonder if the implementation can be improved.
https://www.gnu.org/software/emacs/manual/html_node/calc/Root-Finding.html
suggests that there are some cases where calc will switch over to the
bisection method.  Perhaps the heuristics can be tweaked?


> One thing that can happen is running out of stack, because many of the
> implementations like math-newton-root are recursive. This should be
> easy to remedy as they all seem to be tail calls.

Good to know.