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From: carlc@tektronix.UUCP (Carl Clawson)
Newsgroups: net.math,net.micro,net.micro.pc
Subject: Re: simplex algorithsm for curve fitting---any disadvantage ??
Message-ID: <6563@tektronix.UUCP>
Date: Fri, 14-Feb-86 11:34:05 EST
Article-I.D.: tektroni.6563
Posted: Fri Feb 14 11:34:05 1986
Date-Received: Sun, 16-Feb-86 08:44:38 EST
References: <1217@princeton.UUCP> <11800@ucbvax.BERKELEY.EDU>
Reply-To: carlc@tektronix.UUCP (Carl Clawson)
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In article <11800@ucbvax.BERKELEY.EDU> weemba@brahms.UUCP (Matthew P. Wiener) writes:
>>The authors claimed that the program could fit *any* equation with *any*
>>number of parameters and variables to experimental data.
>
>I don't know the algorithm, but the claim is garbage.  It is impossible to
>fit for a,b,c,d from data points to the function y=a*exp(b*x)+c*exp(d*x).
>The fitting process here is completely unstable.  (I believe this example
>is due to Wilkinson in the late 1950s.)

If the parameters b and d are not "too close," and if you have data
well beyond the "knee" in a log plot of y vs. x, then curve-fitting
works for this case.  I'm not talking about stability theory, I'm
talking about what I've observed.  For arbitrary b,d this is a tough
problem; unfortunately, it is common in radioactive decay, spectroscopy,
and many other fields.

There are other ways of treating it than curve fitting.  See D.N.
Swingler, IEEE Trans. on Biomedical Engineering, BME-24, p.408, July
1977.

I expect to be severely scorched by serious numerical analysts.
Go ahead, send me your proofs of instability, or your flames, or whatever.
-- 
Carl Clawson
Solid State Research Lab / Tek Labs
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(503) 627-6304