Path: news.mathworks.com!newsfeed-00.mathworks.com!nlpi057.nbdc.sbc.com!prodigy.net!flph199.ffdc.sbc.com!prodigy.com!flpi107.ffdc.sbc.com!flpi149.ffdc.sbc.com.POSTED!bba5edff!not-for-mail
From: "W. Dale Hall" <wdunderscorehallatpacbelldotnet@last>
User-Agent: Mozilla/5.0 (Windows; U; Windows NT 6.0; en-US; rv:1.8.1.19) Gecko/20081204 SeaMonkey/1.1.14
MIME-Version: 1.0
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?
References: <f6ebcf2b-4782-4984-aebc-7cdb5b28ccee@p2g2000prf.googlegroups.com>
In-Reply-To: <f6ebcf2b-4782-4984-aebc-7cdb5b28ccee@p2g2000prf.googlegroups.com>
Content-Type: text/plain; charset=ISO-8859-1; format=flowed
Content-Transfer-Encoding: 7bit
Lines: 56
Message-ID: <tJawl.13131$pr6.12098@flpi149.ffdc.sbc.com>
NNTP-Posting-Host: 70.137.171.175
X-Complaints-To: abuse@prodigy.net
X-Trace: flpi149.ffdc.sbc.com 1237399513 ST000 70.137.171.175 (Wed, 18 Mar 2009 14:05:13 EDT)
NNTP-Posting-Date: Wed, 18 Mar 2009 14:05:13 EDT
Organization: at&t http://my.att.net/
X-UserInfo1: OP\[RAGDTBUKBFH[OZK@_TDAYZOZ@GXOXR]ZMVMHQAVTUZ]CLNTCPFK[WDXDHV[K^FCGJCJLPF_D_NCC@FUG^Q\DINVAXSLIFXYJSSCCALP@PB@\OS@BITWAH\CQZKJMMD^SJA^NXA\GVLSRBD^M_NW_F[YLVTWIGAXAQBOATKBBQRXECDFDMQ\DZFUE@\JM
Date: Wed, 18 Mar 2009 10:58:53 -0700
Xref: news.mathworks.com comp.soft-sys.math.maple:24550 sci.math:1160934 sci.op-research:29212 sci.math.num-analysis:107032 comp.soft-sys.matlab:525938


excellentfeng@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 everyone is asking:

	Is this trip necessary?

The next questions are based on an affirmative answer to the first:

	Do any useful transforms Tf (T: Fourier, Laplace,... [there must
	be others with useful expressions for T(derivative)]) exist?

		If so, look at T(f^(200)). Once you have T(f), this
		should be the trivial step.

	What about the inverse transform of T(f^(200))? How ugly is it?

Just my two bits' worth.

Dale