Path: news.mathworks.com!newsfeed-00.mathworks.com!nlpi057.nbdc.sbc.com!prodigy.net!news.glorb.com!postnews.google.com!q9g2000yqc.googlegroups.com!not-for-mail
From: amzoti <amzoti@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 10:18:48 -0700 (PDT)
Organization: http://groups.google.com
Lines: 49
Message-ID: <c1b15d34-b4fa-4795-a5e1-08d15e205682@q9g2000yqc.googlegroups.com>
References: <f6ebcf2b-4782-4984-aebc-7cdb5b28ccee@p2g2000prf.googlegroups.com>
NNTP-Posting-Host: 199.106.59.189
Mime-Version: 1.0
Content-Type: text/plain; charset=ISO-8859-1
Content-Transfer-Encoding: quoted-printable
X-Trace: posting.google.com 1237396728 22969 127.0.0.1 (18 Mar 2009 17:18:48 GMT)
X-Complaints-To: groups-abuse@google.com
NNTP-Posting-Date: Wed, 18 Mar 2009 17:18:48 +0000 (UTC)
Complaints-To: groups-abuse@google.com
Injection-Info: q9g2000yqc.googlegroups.com; posting-host=199.106.59.189; 
	posting-account=HaopWgoAAADs72-s8RQYwP_-ruRUuNzX
User-Agent: G2/1.0
X-HTTP-UserAgent: Mozilla/5.0 (Windows; U; Windows NT 5.1; en-US; rv:1.9.0.7) 
	Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe)
Xref: news.mathworks.com comp.soft-sys.math.maple:24549 sci.math:1160929 sci.op-research:29211 sci.math.num-analysis:107031 comp.soft-sys.matlab:525926


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!

The first question is what the heck are you doing?

If you have a formula, you can use a CAS like Mathematica and ask it
for the 200th derivative and see if it converges on returning a
formula. of course, that in itself might be suspect. If you are
strictly using numerical methods - toss this statement out the window
and re-evaluate what you are asking for because on the surface it
sounds nonsensical.

~A