Regression of complex-valued functions

<SNIP>

Using the same starting values, the two approaches bring to slightly different solutions:

### 1. Real part and Imaginary part

fit$estimate

  [1] -3.8519181 -2.7342861 -1.4823740  1.7173982  4.4529298  1.4383334  0.1564904  0.4856774  2.2789567  3.9011926  0.1227758

### 2. Modulus and argument

fit$estimate

  [1] -3.8674680 -2.7250640 -1.4574350  1.6447868  4.4355748  1.2400092  0.1574215  0.4731295  2.0624878  3.7526197  0.1161640

Do you believe this is due only to ?numerical" reasons linked to how the nls() function works?

I find it a bit surprising that there are differences in the third 
decimal place here.  I would have thought that the results would be 
exactly the same, or ***very*** close to it.

If you have done it right (I have not checked your code at all) the "two 
approaches" should amount to the same approach.  I.e. Mod(z)^2 is
equal to Re(z)^2 + Im(z)^2.

Check your code carefully.

Also it would be a good idea to try a "toy example", something much less 
complicated than your real problem, and see what happens there.

cheers,

Rolf Turner