Quote:
Originally Posted by CaptainBlack  There are at least two answers to this (assuming a is a known numeric value)
1. Set up a model in Excel and use the solver to minimise: ![\int_{t=0}^T [e^{at}-(a't+b')]^2 dt](http://www.mathhelpforum.com/math-help/latex2/img/dc905dc70fc7864d4bdbcd9d53bc47f6-1.gif "\int_{t=0}^T [e^{at}-(a't+b')]^2 dt")
of course this will be discretised so you will have to find  that minimises: ![\sum_{t_i} [e^{at_i}-(a't_i+b')]^2](http://www.mathhelpforum.com/math-help/latex2/img/7b2992bc6c0f6c3974acae9d2d231b65-1.gif "\sum_{t_i} [e^{at_i}-(a't_i+b')]^2")
2. Expand  in orthogonal polynomials on  stopping at the linear term.
CB |
I have run method 2 through Maxima and the results are shown in the attachment (I ought to condense this down to a function definition since this is at least the second time I have done this).
(this is just using Gram-Schmidt to find the first few orthogonormal basis polynomials then using the first couple of terms of the generalised Fourier series corresponding to the orthonormal basis - note I am using the inner product of real functions not that for complex)
CB