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Given a linear system of equations $y=Ax$, the solution to the Lest Squares problem is the vector $\hat{x}$ that minimices the vector $r=y-A\hat{x}$. In my case, I am working in a problem in which I want to minimice the difference between the vector $r^{2}$ (this is, the vector of the elements of $r$ square) and a vector $m$ in which all the elements of the vector have the same value. I am trying to derive the expression but I got nothing. Does someone know how to do it?

Thanks!!

Rodrigo Serna Pérez
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  • Is $m$ given? You want to minimize the norm of $r - m = y - m - A x$. (We are minimizing with respect to $x$.) Just let $b - y - m$ and minimize the norm of $b - Ax$ (with respect to $x$). – littleO Jan 04 '17 at 12:19
  • I have edited the question, I did an error describing the problem. – Rodrigo Serna Pérez Jan 04 '17 at 12:22
  • Oh ok. I'm still not sure if $m$ is given in advance or not, though. Do you know in advance the exact value of $m$? – littleO Jan 04 '17 at 12:28
  • Yes, $m$ is given. What I want to do is getting $\hat{x}$ so the power of the vector $r$ is as close as possible to certain known constant. – Rodrigo Serna Pérez Jan 04 '17 at 12:31
  • Do you mean you want the vector with the least variance (Hence constant)? – Royi Sep 09 '17 at 14:14

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