Landweber spectral filter
= Landweber spectral filter
{c}
{title2=$f_n(\sigma)=1-(1-\tau\sigma^2)^n$}
Starting <Landweber iteration> at zero gives
$$
x_n=\sum_j\frac{1-(1-\tau\sigma_j^2)^n}{\sigma_j}\langle y,u_j\rangle v_j
$$
in a <singular system of a compact operator>. The dimensionless damping filter is $f_n(\sigma)=1-(1-\tau\sigma^2)^n$. If the full inverse coefficient is called the filter instead, it is $f_n(\sigma)/\sigma$; these conventions describe the same operator.