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From: pnachtwey <pnachtwey@gmail.com>
Newsgroups: comp.soft-sys.math.maple,sci.math,sci.op-research,sci.math.num-analysis,comp.soft-sys.matlab
Subject: Re: How to take 200th order derivative, and then evaluate it 
	numerically?
Date: Wed, 18 Mar 2009 11:12:42 -0700 (PDT)
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On Mar 18, 9:42=A0am, excellentf...@gmail.com wrote:
> Hi all,
>
> We need to take the 200th order derivative of a complicated formula,
> and then evaluate it numerically.
>
> What's the best way to handle this?
>
> More specifically, we figured that it's impossible to do this via
> finite difference, i.e. do everything completely in the numerical
> domain, because the noise will be huge and error will dominate.
>
> So a plan was to first obtain the 200th order derivative thru symbolic
> calculation in Maple, Matlab, Mathematica, and then copy the huge
> result and somehow make it into a form that is numerically evaluable
> either in Matlab or C++. Then evaluate that huge expression
> numerically. Still, that sounds daunting, the symbolic result of 200th
> order derivative will be huge and we are not sure if Maple or
> Mathematica can handle it.
>
> Another possibility is to do some sort of Automatic Differentiation.
> But we are new to AD. Is it possible that with the help from an AD
> package, we just need to give inputs of the parameter values, and the
> package will crank out the numerical result of the 200th order
> derivative with almost no error?
>
> We see that lots of free packages are in C/C++ or Fortune, which are
> not convenient for fast prototyping(we are at evaluating stage, if
> this idea doesn't work, we don't want to spend too much time on it).
> So are there free AD packages that can go with Matlab or Mathematica
> or Maple that can take 200th order differentiation and are convenient
> for prototyping? Which one is the best AD package that we could try
> on? If it doesn't work, then we would discard this crazy idea of
> taking 200th order derivative completely.
>
> Please shed some lights on us!
>
> Thanks a lot!
How did you even get the coefficients for a 200th order polynomial?

I agree with the others that say this is non sense. Any number, that
is not extreme close to 1 taken to the 200 power, will either cause a
numeric overflow or be rounded down to 0 unless you have a very high
precision calculator.

However, if the equation is a 200th order polynomial then one can
compute the coefficients for any of the derivative functions easily
enough in C or Fortran.  Then the equation can be evaluated using
Horner's method.  No matlab, mathematica or maple required.  I have
done this before with 5 to 7th order polynomials. It would be easy
enough to expand the arrays to do this with 200th order polynomials.

Peter Nachtwey