Nonlinear least squares fit to determine Constants in given Formula

So I have the following two equations:

(1)

(2)

Here x =

I have a set of data points that is

I know as it is a constant.

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

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

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 .

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)

(2)

Here x =

I have a set of data points that is

I know

as it is a constant.

My question is how do I use a nonlinear least squares method to get values for

and

.

What I've tried so far is solving for x in equation (2) using the quadratic formula and likewise solving for

in equation (1). From there, I equated the two resulting equations since x =

and then solved for F, so I get some equation that is F =

.

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

.

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