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elgen
Posts:
7
Registered:
8/27/10


Re: Leastsquare optimization with a complex residual function
Posted:
Oct 30, 2010 11:16 AM


On 101029 02:44 AM, kym@kymhorsell.com wrote: > elgen<sket16@no.spam.hotmail.com> wrote: > ... >> How would I proceed to calculate its gradient? Would you mind being more >> specific? What is "SoS"? > > Sum of Squares. A quite usual term when working in least squares. > > If you have sum_i (x_i^2+y_i^2) you are saying you can not compute the > partial derrivatives wrt all the x_i and y_i? > > If not, I'm sorry, it's sounding like some kind of assignment > and I'm in the habit of only giving minimal hints. >
I am working on a project to optimize the timeharmonic electromagnetic field, which is a complex quantity. As I didn't have complex analysis in the undergraduate years, differentiation and integration involving complex numbers do not make me feel very comfortable. I am slowing picking up things along the way.
I get the idea that the conjugated inner product makes the residual real. So the problem is to find the gradient of the real function with respect to its complex argument z, i.e. x_i(z) and y_i(z). My feeling is that I need to take the differentiation with respect to the real(z) and imag(z).
Wait a second ... as the residual is a real function of a complex argument, would the residual be analytic? Could I directly take the derivative with respect to z without heeding its real and complex part?
Thank you for the previous hints. That has made my way to complex analysis a little easier.
elgen



