Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 326 / 1 / 1 / 3 / a / Solution

Repeated substitution in Landweber iteration from $u_0=0$ givesOn the $i$th singular vector, $A^{\ast }A$ has eigenvalue ${\sigma }_i^2$ and $A^{\ast }{y}_i={\sigma }_i{x}_i$. The finite geometric series therefore givesThis is a spectral regularization method with filter