Iterated Tikhonov regularization

Iterated Tikhonov regularization repeatedly applies a filtered correction based on $A^{\ast }(y-A{x}_n)$. Its singular-system representation exposes the iteration as a family of scalar spectral filters.

The implicit iteration $(I+\tau K^{\ast }K)u_{k+1}=u_k+\tau K^{\ast }f$, starting from zero, multiplies each data singular vector by $[1-(1+\tau {\sigma }^2{)}^{-k}]/\sigma$. Its operator norm is at most $\sqrt{k\tau }$.