Tikhonov regularization

Tikhonov regularization minimizesgiving $x_{\alpha }^{\delta }=(A^{\ast }A+\alpha I{)}^{-1}{A}^{\ast }{y}^{\delta }$. The spectral filter $\sigma /({\sigma }^2+\alpha )$ suppresses unstable division by small singular values.

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.