The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Least-square optimization with a complex residual function
Replies: 4   Last Post: Oct 30, 2010 11:16 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]

Posts: 7
Registered: 8/27/10
Re: Least-square optimization with a complex residual function
Posted: Oct 30, 2010 11:16 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On 10-10-29 02:44 AM, wrote:
> elgen<> 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 time-harmonic 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

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.


Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.