= Tikhonov filter norm bound
{c}
{title2=$\|(K^*K+\alpha I)^{-1}K^*\|\leq1/(2\sqrt\alpha)$}
For a <bounded linear operator> between <Hilbert spaces>, the <spectral regularization method> for quadratic <Tikhonov regularization> has scalar coefficient $s/(s^2+\alpha)$. Since $(s-\sqrt\alpha)^2\geq0$, this coefficient is at most $1/(2\sqrt\alpha)$. The <spectral theorem for normal operators> transfers this scalar bound to the <operator norm>, providing the noise term in the <noise-bias decomposition for linear regularization>.
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