It may be the silliest question but... why is the stopping criterion of rtflsp based on "del" and not on dx as most books (and my common sense) would have ?

Similarly, the first stopping criterion in zriddr, based on "xnew-ans", hardly makes sense to me (whereas the 2nd one, based on "xh-xl" does)

Many thanks in advance
Michel

I think the problem is that the Reguli Falsi method does not bracket the root, it approaches from one side depending on the curvature of the function.

Thank you, Integral, for trying.

However, regula falsi, precisely, does keep a bracket, in opposition to the
secant method.

It also doesn't solve the Ridders riddle.

I can understand that either Reg Falsi
or Ridders could get stuck, to the point that one would just want to exit. But
why exit with a solution, and not with
a "no solution found to desired tolerance", then ?

Michel

Dear Michel,

The idea in both cases is to base the stopping criterion on whether the last update was sufficiently small. This is theoretically likely to lead to an earlier termination than simply monitoring the width of the bracket, although in practice I doubt it makes a big difference.

Saul Teukolsky

Dear Saul,

Many thanks for your reply.
In my application, the Ridders "got-stuck" criterion does kick in, although the "bracket-width" criterion would stop the algorithm a few iterations later. No catastrophy, but with the first criterion I do get a solution that is slightly less than the required precision. I just need to be aware of that.

And thank you for the forum: I find very satisfying the idea of being able to discuss a recipe with other users, when I fail to solve the problem myself.

Best regards,
Michel