Is There a Formula for Fitting a Sum of Exponentials to Data Points?

[Gonzolo]

Hi, I want fit the following equation to a set of data points :

$$y = A(exp(-Bx)-exp(-Cx)))$$

I found how to determine A and B for one exp : y = Aexp(-Bx), but I'm not sure if there's a formula for A, B and C in such a sum (or difference) of exponentials. Thanks.

 

[HallsofIvy]

There isn't a formula but there is a general concept:
$$y = A(exp(-Bx)-exp(-Cx)))$$
has 3 undetermined constants, A, B, and C so you will need to solve three equations for them. Take three of your (x,y) data points and plug the values for x and y into the formula. Solve those three equations for A, B, C.

If you have more than 3 data points, and the formula is not and exact fit, the result will depend upon which 3 you choose.

 

[Gonzolo]

I have tried to fit using the least squares method (with Excel) and that is what I find, that the results depend on what initial values I choose. So if what your saying in your last sentence is generally true, I suppose there no way to find the absolute minimum of the least squares sum, right?

If by exact, you mean that each data point should be on the curve exactly, then no it cannot be exact, since it is true experimental data, and there is a little noise.

Is there a way to determine an error for A, B, and C on the best fit that I choose?