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