Hi Yannick,

>
> About the default value (1e-14), I know the tolerance is case-dependant, but 
> some times, we don't precisely know the order of magnitude (ex : jacobians 
> matrices) and it's quite practical to have a default value.
> In our tools, we use this value in the test classes, but also for specific 
> algorithm convergence threshold.
>
I'm uncomfortable with CM having a default tolerance implemented
somewhere. As you said, tolerances are case-dependant, and therefore
DEFAULT_TOL (or whatever you want to call it) should stand in your
particular application, not in a utility Commons-Math class. This is
pretty much the approach adopted in our testing suites. You will
frequently find a constant field with a default tolerance which
applies for the specific unit test only. I would be very reluctant to
try and be more general, while we all know that such a constant would
not mean anything.

Don't mistake me. I'm not saying that chosing a (somewhat arbitrary)
default tolerance is bad practice. As you said, sometimes there is no
other option.

I would like to know what others think,
Sébastien


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