Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Gradient of a complex expression

  1. Dec 7, 2011 #1
    My question is concerning how to compute the complex gradient of the following cost functional with respect to W:

    F=Ʃ_i=1:M ||y_i-Go*W_i||^2 + Ʃ_i=1:M ||W_i - X*(E_i - Gc*W_i)||^2

    Where the summations go from i=1 to i=M and the dimensions of the diferent elements are:
    y: Nx1
    Go: Nxn
    W: nx1
    And ||..||^ 2 indicates the square norm.
    The elements of the different matrix and vectors are complex numbers

    My problem is that I need to compute the gradient to apply a conjugate gradient minimization algorithm to minimize the cost functional. Any help or reference about how to compute gradients of this type of expressions (vectors and matrix) will be appreciated.
    Thank you very much.
    Last edited: Dec 7, 2011
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted

Similar Threads for Gradient complex expression
A How to Convert a Complex Logarithm to a Complex Exponential
I Complex integral