= Tikhonov stability bound
{c}
{title2=$\|(A^*A+\alpha I)^{-1}A^*\|\leq(2\sqrt\alpha)^{-1}$}
The reconstruction operator in <Tikhonov regularization> has scalar gain $\sigma/(\sigma^2+\alpha)$. Its maximum over $\sigma\geq0$ is $1/(2\sqrt\alpha)$, so a data perturbation of norm at most $\delta$ changes the solution by at most $\delta/(2\sqrt\alpha)$. A convergent noisy-data parameter choice satisfies $\alpha\to0$ and $\delta/\sqrt\alpha\to0$. Fixed-parameter stability is distinct from stability of the unregularized inverse.
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