Just because we the creators of the framework see no need for higher order derivates, the end users, whose needs no one can fully enumerate, may have a quite reasonable use for them.
Well, I designed the interface as a helper for a variety of numerical algorithms, not for general use. It's the way the user supplies his function to solvers. Solvers rarely need higher derivatives. If a solver has to use a third or higher derivative, we can still extend the interface. If someone else wants to use an algorithm which needs higher derivatives, he can use his own mechanism or extend what is available on his own.
If you create a function, you control the implementation for creating the derivative function object and is directly coupled to your object. The implementor, you,
Not quite. I expect a variety of prebuild function objects and perhaps some mechanisms for more generic definition of functions, but if push comes to shove, it's the user of j-c-math who has to code a class for supplying his function to the solver. I want to think him of the calculations to be closely related.
[rearranged]
Why can't the domain of interest and explicit input be a single value? That's exactly how I did the CDF stuff using a root finding method which needs a bracket and it worked fine. And it's a generic process that could be incorporated into all the solvers.
Nice, build a modular system: an interval(or bracket)-from-start-value builder and solvers which need an interval (or more likely a bracket). You can provide convenience objects which combines everything.
> When did I introduce finding all roots into this discussion?
You didn't. A solver might not find the root closest to the start value, with no indication that there is a root closer to the start value than the reported root. I mean something like start value 0, expected root near 0.5, reported root 1E15. I wager a guess this will irritate a few people. OTOH, letting the solver do heavy checking every time just in case may be seen as an unnecessary overhead to more advanced users, and because this *will* be equivalent to the problem of finding *all* roots in general, it is often impossible. Note that the most difficult part in root finding is not finding the root, but detecting when you stray out of the domain of applicability of the algorithm and detecting ill conditioned problems.
Having the user to supply an interval is no guarantee that he knows what he is doing, but if the interval size is much larger than the required accuracy suggests, implementations could just bail out.
J.Pietschmann
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