Very strange behavior.

Hi Viacheslav. Numerical procedures: You can always find examples where they fail. I find this variation of your example particularly worrisome since the function changes sign in the interval where the zeros are requested. It seems that it takes as a tolerance something proportional to the width of the interval



It is true that apparently the SMath algorithm can be improved in several ways. However, something good must have. Here SMath succeeds where Maple, Maxima and FindRoot do not.



solve_bug.sm (9 KiB) downloaded 118 time(s).

Best regards.
Alvaro.

Wrote

Very strange behavior.

I may have written about this bug long time ago.
Solve Calculates Different With Different Ranges

Wrote

Very strange behavior.

Often, strange behavior results from numerical instability.
I have observed that fact between MCD 11 XP 32 bits vs same SS 6179 32 bits.
The best example is the Mathematica 4.0 famous function.
Solving the Goat radius is another example ... no way for 15 decimals !
Mathsoft Minerr uses a specific technique to cope with this fact,
i.e: fool two similar results by injecting a small random.
As well, Smath solvers turn unstable, pedal within their own end iterate.
You forgot to show the function.
Cheers ... Jean.