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Math Help - [SOLVED] best fit of exponential function

  1. #1
    roeppieroeppie
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    [SOLVED] best fit of exponential function

    Hi,
    I am looking to fit a set of data with the following exponential.

    y = a + b*exp(-x/c) + (d*x/c)*exp(-x/c) with x>0.

    So i would like to find the best four values for the parameters a to d.
    I am trying to work out something with a least squares method but I am not sure how to start (problems with how to weight y). Does anyone have an idea here?

    Any answer would be highly appreciated!
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  2. #2
    hpe
    hpe is offline
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    Quote Originally Posted by roeppieroeppie
    Hi,
    I am looking to fit a set of data with the following exponential.

    y = a + b*exp(-x/c) + (d*x/c)*exp(-x/c) with x>0.

    So i would like to find the best four values for the parameters a to d.
    I am trying to work out something with a least squares method but I am not sure how to start (problems with how to weight y). Does anyone have an idea here?

    Any answer would be highly appreciated!
    This calls for a numerical approach. Using a simple derivative-free method (Nelder-Mead) might be enough. In Matlab this is implemented as "fmins". Redo the computation a number of times to see if the solution depends on the start data (there may be more than one solution for such a problem).

    A fancier method would be a Gauss-Newton method - it requires more programming, however.
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