Early stopping of Landweber iteration

The Landweber spectral filter progressively admits smaller singular-value components. Its approximation bias tends to zero on exact admissible data, but its noise amplification grows. With $\Vert A\Vert \le 1$, a sufficient a priori regularization parameter choice is $n(\delta )\to \infty$ and $\sqrt{n(\delta )}\delta \to 0$. Taking regularization parameter $\alpha =1/n$ expresses this as $\alpha \to 0$ and $\delta /\sqrt{\alpha }\to 0$; the noise-bias decomposition for linear regularization proves convergence.