Curve-fitting sums of exponentials: variation on the theme

Tue Sep 7 10:18:02 EST 1993

Following up this comment recently posted to Bio-Soft, on the matter 
of curve-fitting sums of exponentials....

> Be careful.  Fitting general sums of decaying exponentials is an
> ill-conditioned problem for which one is usually cautioned against
> general least-squares routines.  

Hmm, is it possible that some of the ill-conditioning arises from 
the application of straightforward least-squares itself? Or is the 
ill-conditioning completely intrinsic to the sum-of-exponentials 
model itself? In any event, a variant approach to this curve-fitting 
problem has received attention in recent years, and it is claimed to 
have certain advantages over the usual approach:

	Herbert R. Halvorson (1992)
	Pade'-Laplace algorithm for sums of exponentials: Selecting 
		appropriate exponential model and initial estimates 
		for exponential fitting
	in, "Numerical Computer Methods"
	Ludwig Brand & Michael L. Johnson, eds.
	Methods in Enzymology 210: 54-67

	E. Yeramian & P. Claverie (1987)
	Analysis of multiexponential functions without a hypothesis 
		as to the number of components
	Nature (12 March 1987) 326: 169-174

	P. Claverie & A. Denis (1989)
	[I don't know the title]
	Computer Physics Reports 9(5): 247-299
	[contains details of Claverie et al's Pade'-Laplace approach 
		to fitting sums of exponentials]

I cannot assure anybody of this alternate approach's merit, as my 
awareness of it is only superficial. Still, it seems to be relevant 
and may be worthy of investigation.

	Mark Reboul
	Columbia-Presbyterian Cancer Center Computing Facility
	mark at cuccfa.ccc.columbia.edu

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