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I would like to least square fit a number of measurements using several nonlinear functions with shared parameters (similar to the advanced fitting in Origin) using Mathematica.

Therefor I would be interested in an Algorithm like Gauss-Newton that fits several data-set to several functions (with shared parameters) "in parallel".

For example, I would like to fit the set of functions f1=a*exp(c1/x) ... fn=a*exp(cm/x) to a number of giving data-sets y1(x1,...,xm) ... yn(x1,...,xm). As indicated all "a" in f1...fn should have the same value while c1...cn differ.

Unfortunately, I can not find a suited algorithm on the Internet and I have a hard time adopting the algorithms fitting one function to one set of data.

I would appreciate any help, links or references that cover the given topic.

Thank you very much for your help!

Best regards,

Sebastian