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
Least-square optimization with a complex residual function
Posted: Oct 28, 2010 9:10 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

I have a question on the least-square optimization with a complex
residual function. The residual function is r(z_1, z_2), in which z_1
and z_2 are complex variables.

The LS cost function is

\sum_i ||r(z_1, z_2||^2

where i is the number of samples.

Many textbooks discusses this problem in the context of a real residual
function and || \cdot || denotes the euclidean norm.

In my case r(z_1, z_2) is a complex function. If I use the Euclidean
norm (conjugated inner product), the cost function becomes

\sum_i conj(r)r

I am stuck on how to calculate the gradient of this cost function as
conj(r) is not an analytic function and the gradient needs to take the
derivative with respect to z_1 and z_2.

Any feedback is welcome. Thank you.


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.