We Know that To minimize the sum of error (objective Function)
$\ J = (y(t)-\theta (t) u(t))^2 $ (eq. 1)
is done by using least square :
$\theta (t) = \theta (t-1) + \gamma y(\theta u -y) $ (eq.2)
Where $u=input ; $ $y=output; $ $\theta=Gain Input; $ $t=time; $
But the question is how to prove that eq.2 is minimizing the eq 1 respect to $\theta$?
and what the terms that shows $J$ is minimized ?
*Lets say all variables is scalar