How to find parameters of implicit function?

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Jernej 2014-6-18

I have to find parameters a and b of this implicit function y=1614413.7*(coth((x+b*y)/a)-a/(x+b*y)).

This function best describes my data. So far I have written this code:

function y=deviskaF(x,p)

y=zeros(size(x)); NN=length(x); opt=optimset('display','off');

for i=1:NN y(i)=fsolve(@(y) y-1.5e6*(coth((x(i)+p(2)*y)./p(1))-(p(1)./(x(i)+p(2)*y))), .1, opt); end end

Then I call this function in lsqcurvefit in matlab command window.

lsqcurvefit(@(params, xdata) deviskaF(xdata,params),[10 1e-6], x, y)

Parameter a should be somewere around 10 and parameter B around 10^-6. The results are far away from predicted results and I also get this message:

Local minimum possible.

lsqcurvefit stopped because the size of the current step is less than the default value of the step size tolerance.

What am I doing wrong?

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