I thought maybe my suggestion for reparameterizing this simple problem
was ignored because I didn't supply R code for the problem.
Here it is using optim for the optimization. It converges trivially with
an initial value for E of 1000.
As I stated before, there is nothing at all difficult about this
problem. You simply need to parameterize it properly. Of course that is
not to say that rescaling is not useful as well, but the important thing
is to parameterize the model properly.
ExponValues=c(2018.34,2012.54,2018.85,2023.52,2054.58,2132.61,2247.17,2468.32,27
78.47)
Expon=c(17,18,19,20,21,22,23,24,25)
# Example starting estimate calculation
E=1000.0
y1=2018
yn=2778.47
nobs=9
#keep y1 and yn fixed and get initial value for E
Esp1 <- optim(c(E=E),method ="BFGS",
function(x)
{
E=x[1]
a=(yn-y1)/(E^Expon[nobs]-E^Expon[1])
Y0=y1-a*E^Expon[1];
diff=ExponValues-(Y0+a*E^ExponCycles)
return(1000*sum(diff*diff))
})$par
E=Esp1[1]
Esp <- optim(c(y1=y1,yn=yn,E=E),method ="BFGS",
function(x)
{
E=x[3]
a=(x[2]-x[1])/(E^Expon[nobs]-E^Expon[1])
Y0=x[1]-a*E^Expon[1];
diff=ExponValues-(Y0+a*E^ExponCycles)
return(1000*sum(diff*diff))
})$par
y1=Esp[1]
y2=Esp[2]
E=Esp[3]
a=(y2-y1)/(E^Expon[nobs]-E^Expon[1])
Y0=y1-a*E^Expon[1];
--
David A. Fournier
P.O. Box 2040,
Sidney, B.C. V8l 3S3
Canada
Phone/FAX 250-655-3364
http://otter-rsch.com
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