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Math Help - Nonlinear least squares fit to determine Constants in given Formula

  1. #1
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    Nonlinear least squares fit to determine Constants in given Formula

    So I have the following two equations:

    (1) F = F_0 (C_t - C_b) + F_b C_b
    (2) Kx^2 - x(KD +KC_t +1) + KD C_t = 0

    Here x = C_b

    I have a set of data points that is  (F_i, D_i)

    I know C_t as it is a constant.

    My question is how do I use a nonlinear least squares method to get values for F_0 , F_b , and  K .

    What I've tried so far is solving for x in equation (2) using the quadratic formula and likewise solving for  C_b in equation (1). From there, I equated the two resulting equations since x = C_b and then solved for F, so I get some equation that is F =  f(K, C_t, F_0 , F_b) .

    Is this even going in the right direction? I am trying to create a MATLab program that will help in solving for these parameters, as it's something I'm going to have to solve for many data sets  (F_i, D_i) .

    Additionally, does anyone have any recommendations for textbooks I can reference in solving a problem like this as I'm at a bit of a loss in trying to solve this?
    Last edited by tantile; November 28th 2011 at 12:46 AM. Reason: Error in expression fixed!
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  2. #2
    Grand Panjandrum
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    Re: Nonlinear least squares fit to determine Constants in given Formula

    Quote Originally Posted by tantile View Post
    So I have the following two equations:

    (1) F = F_0 (C_t - C_b) + F_b C_b
    (2) Kx^2 - x(KD +KC_t +1) + KD C_t

    Here x = C_b

    I have a set of data points that is  (F_i, D_i)

    I know C_t as it is a constant.

    My question is how do I use a nonlinear least squares method to get values for F_0 , F_b , and  K .

    What I've tried so far is solving for x in equation (2) using the quadratic formula and likewise solving for  C_b in equation (1). From there, I equated the two resulting equations since x = C_b and then solved for F, so I get some equation that is F =  f(K, C_t, F_0 , F_b) .

    Is this even going in the right direction? I am trying to create a MATLab program that will help in solving for these parameters, as it's something I'm going to have to solve for many data sets  (F_i, D_i) .

    Additionally, does anyone have any recommendations for textbooks I can reference in solving a problem like this as I'm at a bit of a loss in trying to solve this?
    Please correct/complete (2) as it is it is just an expression.

    CB
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  3. #3
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    Re: Nonlinear least squares fit to determine Constants in given Formula

    Quote Originally Posted by CaptainBlack View Post
    Please correct/complete (2) as it is it is just an expression.

    CB
    Sorry about that! Fixed, it should be equal to 0
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