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Y I
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How to solve linear least squares problem of the following form in matlab

Asked by Y I
on 3 Dec 2018 at 23:35
Latest activity Commented on by Walter Roberson
on 8 Dec 2018 at 23:14
Hello
  1. I need to solve the problem which is written in the following form:
1.JPG
I have all the terms except ws, which I need to find. Firstly I don't understand how I can rewrite this problem in the following way Ws = ... Is it possible?
And how to solve this problem in Matlab? I did not find suitable function which corresponds to this form...
2. From the same article:
2.JPG
I don't have any idea how they rewrite this but how to solve this problem in this form?
What I found in Matlab is:
3.JPG
But what does it mean this 2 at the bottom and can I use this function to solve equation (3)?
Since H and h are the matrices, so can I write in matlab vector A which contains another matrices?
Thank you!

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1 Answer

Answer by Walter Roberson
on 4 Dec 2018 at 0:29
 Accepted Answer

||expression|| with subscript 2 means the 2-norm, also known as the Euclidean distance. With the Euclidean distance being sqrt() of a sum of squares, and with the result of the 2-norm being squared by lsqnonneg, what is being computed is effectively the sum of squares.
Likely this is the same thing that your equation means with ||expression|| squared with no subscript 2, so Yes, lsqnonneg is a plausible function.

  6 Comments

Are your ws permitted to be complex valued? Are they permitted to be negative?
Yes, ws are permitted to be complex and negative.
Then Yes, it looks to me as of you can use the \ operator.
MATLAB offers multiple methods of solving problems.

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