Nonlinear least squares fit to determine Constants in given Formula

So I have the following two equations:

(1) $\displaystyle F = F_0 (C_t - C_b) + F_b C_b$

(2) $\displaystyle Kx^2 - x(KD +KC_t +1) + KD C_t = 0$

Here x = $\displaystyle C_b$

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

I know $\displaystyle C_t$ as it is a constant.

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

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

Re: Nonlinear least squares fit to determine Constants in given Formula

Quote:

Originally Posted by

**tantile** So I have the following two equations:

(1) $\displaystyle F = F_0 (C_t - C_b) + F_b C_b$

(2) $\displaystyle Kx^2 - x(KD +KC_t +1) + KD C_t $

Here x = $\displaystyle C_b$

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

I know $\displaystyle C_t$ as it is a constant.

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

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

Re: Nonlinear least squares fit to determine Constants in given Formula

Quote:

Originally Posted by

**CaptainBlack** Please correct/complete (2) as it is it is just an expression.

CB

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