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Math Help - how to fit data in this curve

  1. #1
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    how to fit data in this curve

    this is a question that came in final exam
    fit the data in this given curve
    Y=A^exp(cx)+B^exp(dx)

    how to fit any given data in this curve......can any one tell me how to start this question(here you can assume any set of values that we want to fit
    i tried but not able to solve the question
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  2. #2
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    Quote Originally Posted by reflection_009 View Post
    this is a question that came in final exam
    fit the data in this given curve
    Y=A^exp(cx)+B^exp(dx)

    how to fit any given data in this curve......can any one tell me how to start this question(here you can assume any set of values that we want to fiti tried but not able to solve the question
    What tools do you have?

    CB
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  3. #3
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    not using any tool....how to calcuate on paper...pls help....using least suqare method
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  4. #4
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    Quote Originally Posted by reflection_009 View Post
    not using any tool....how to calcuate on paper...pls help....using least suqare method
    There is not enough information, and it is probably impractical on paper anyway.

    CB
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  5. #5
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    Y=A^exp(cx)+B^exp(dx)
    fit the following data using least sqare methos technique
    X=1 2 3 4 5
    Y=3 8 15 28 46

    where A,B,c,d are constants.......this time our university has setted most toughest quesion paper on numerical analysis....this is one of them a question
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  6. #6
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    Quote Originally Posted by reflection_009 View Post
    Y=A^exp(cx)+B^exp(dx)
    fit the following data using least sqare methos technique
    X=1 2 3 4 5
    Y=3 8 15 28 46

    where A,B,c,d are constants.......this time our university has setted most toughest quesion paper on numerical analysis....this is one of them a question

    http://mste.illinois.edu/malcz/ExpFit/FIRSTCURVE.html
    see the above link. i hope it will be useful....otherwise tell me explain more
    i think your problem is noy least square....least squre method is to fit data into a polynomial....you are looking for exponential curve fitting...you can google it and find more information
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  7. #7
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    My guess is that perhaps you cannot "assume any set of values that we want to fit".

    For example if there are 4 or fewer points to fit to then it is possible to get an exact match. If there are more points then it will be an approximation (except for in special cases).

    There may be some clues in that data that you have missed such as the value for y(0) or y'(0), zero crossings or turning points.

    I suggest posting the data from the original question.
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  8. #8
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    could you give me any gusses how to solve the equation......?just make a equations afterthat i will try to solve it
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  9. #9
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    Put C=e^c and D=e^d, then you want to minimise:

    O(A,B,C,D)=\sum_{i=1}^5 (Y_i-(AC^i+BD^i))^2

    Which can in principle be done with pencil and paper, but I would rather not.

    CB
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  10. #10
    A Plied Mathematician
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    Exponent or Multiplication?

    Do you mean Y=A^{e^{cx}}+B^{e^{dx}}, or A e^{cx}+B e^{dx}?
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  11. #11
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    Quote Originally Posted by Ackbeet View Post
    Do you mean Y=A^{e^{cx}}+B^{e^{dx}}, or A e^{cx}+B e^{dx}?
    Good point, that is what the OP writes (but I would still bet what I posted is what he meant - at least until they say otherwise).

    That the data looks very like a polynomial does not help either.

    CB
    Last edited by CaptainBlack; June 4th 2010 at 10:45 AM.
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  12. #12
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    A Start

    Assuming the multiplication is implied, and you have a data set \{x_{i},y_{i}\} for i=1,\dots,n, and the assumption is that y=A e^{cx}+B e^{dx}, then you want to set up your least squares parameter as follows:

    Let \Delta=\sum_{i=1}^{n}(y_{i}-(A e^{c x_{i}}+B e^{d x_{i}}))^{2}.

    Then you set

    \frac{\partial\Delta}{\partial A}=\frac{\partial\Delta}{\partial B}=\frac{\partial\Delta}{\partial c}=\frac{\partial\Delta}{\partial d}=0, and solve for A, B, c, and d.

    This basic idea is how all least squares fits work.
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