Regularization of Deterministic Discretized Inverse Problems

In this chapter, we continue to treat noisy data problems of identification and control under deterministic assumptions on the error of observation. Within Chapter 3, auxiliary problems of minimization type (3.39) and (3–40) have been constructed, the solutions of which continuously depend on the input data. Now we present a family of well-posed optimization problems that represent stable neighbouring problems for the discretized inverse problem under consideration. The idea of dealing with this family of problems goes back to TIKHONOV [428–29]. Therefore, the method considered below in a particular fashion is called Tikhonov regularization method.