equation solving for experimental data

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teresa on 10 Feb 2011
Hi,
I am trying to solve a nonlinear equation (Z(f)) of 4 variables which is the following:
Z=sqrt(((x(1)+x(4)-x(1)*x(2)*x(3)*(2*pi*f)^2)^2+(x(1)*x(2)*x(4)+x(3))^2*(2*pi*f)^2)/(1+x(1)^2*x(2)^2*(2*pi*f)^2))
I've got experimentally 200 pairs of values of Z and f and I would like to find the coeficients x(1), x(2), x(3) and x(4) which introduce the less error into these pairs of values.
Curve fitting seems to work similarly, but I am not sure it will work properly.
Can anybody lend me a hand?
Francesc I. Rillo

Walter Roberson on 10 Feb 2011
It appears that the solution that might perhaps be most suitable for fitting would be,
x(1) = 0
x(4) = 0
x(3) = abs(Z)/(2*Pi*f)
x(2) = 1/ (x(3) * 8*Pi^2 * f^2)
teresa on 11 Feb 2011
I am sorry but I do not understand that solution. I have probably not explained myself properly.
I have 200 experimental values of Z and f. If I do what you suggest I would obtain 200 x(3) and x(2). What I want is to find the value of each one of the 'x' that for my experimental values introduces less error.
In other words. I got (Z1,f1),(Z2,f2),... (Z200,f200). If I obtain some fix values of x(1), x(2), x(3) and x(4) and use the equation I can obtain (Z1',f1), (Z2',f2),... (Z200',f200). I want to do Z1-Z1', Z2-Z2', ... Z200-Z200' the closest to 0 as possible using just a single value for each 'x'.
I have been told there is a toolbox in Matlab that can help me, similar to the working way of the 'fsolve' function.