Equivalence of regularization and truncated iteration in the solution of ill-posed image reconstruction problems (Q751186)

The author considers stable methods for the approximate solution of ill- conditioned systems of linear equations by means of Phillips-Tikhonov regularization, and by means of truncated iterative methods (i.e. iterative methods that are stopped after a fixed number of steps). It is proved that these two (families of) methods are equivalent in the sense that the endresult of a method of one family can be obtained via a process from the other method with suitable smoothing- resp. iteration- matrix. This applies to overdetermined as well as underdetermined systems of linear equations.