You only have ONE data point.
xdata=420;
ydata=0.1;
So only ONE piece of information! How do you intend to estimate TWO parameters anyway?
x0 = [1,1];
Yes, you say that you only want to estimate one parameter. But you are telling lsqcurvefit that there are TWO parameters.
Next, symsum does NOT create a numerical value, thus a double. It creates at best, a SYMBOLIC parameter. You need to convert that to a double.
help double
Next, a must be a negative number, else that series will never converge. It will be a divergent series. So starting the estimation out with a POSITIVE starting value for a will cause the optimization to fail.
Anyway, since you have only one data point, you can just use solve, or actually, vpasolve, since this series is unlikely to have a symbolic solution.
syms n a
xdata=420;
ydata=0.1;
fun = 1-0.608*symsum((1/(n^2))*exp(a*n^2*xdata*246250),n,1,1000)
vpasolve(fun == 0,a)
As you can see, there was no need to use lsqcurvefit.
A fear however, is that as I said, it gives me a positive value for a. That means the series will not in fact converge at all. And THAT means if I use a different number of terms in the symsum, I will get a dramatically different solution.
fun = 1-0.608*symsum((1/(n^2))*exp(a*n^2*xdata*246250),n,1,2000)
vpasolve(fun == 0,a)
Do you see the prediction changed?
I'm sorry, but this suggests there is no solution. So, CAN we push the solver into finding a solution for negative values of a? I'll change the series expression in a subtle way. In fact, if you try various negative values for a there, I cannot get the solver to find any negative value for a that solves the probem, but since the series is truly, factually divergent for positive a, again, there is no solution.
