= Quadratic norm penalty
{title2=$\alpha\|x\|^2$}
A squared <Hilbert space> norm penalizes reconstruction size in <Tikhonov regularization>. For $\alpha>0$, adding $\alpha\|x\|^2$ to $\|Ax-y\|^2$ produces a <strictly convex> <coercive function> with unique minimizer. Its first variation contributes $\alpha x$ to the <normal equation for a linear inverse problem>, shifting $A^*A$ to $A^*A+\alpha I$. It selects a minimum-norm representative and controls amplification of noisy small-singular-value components.
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