Discretization of Inverse Problems

Parameter identification problems can be formulated as equations In many interesting cases, X and Y are infinite-dimensional spaces of functions – this was so for all model problems presented in Chap. 1 Although we generally suppose that a unique solution \(u^{{\ast}}\in \mathbb{U}\) exists, explicit formulae for its computation are only rarely available, so that one has to be satisfied with the construction of an approximate solution by numerical methods. In practice, not even the equation T(u) = w itself is perfectly known, if w is a function. Rather, an approximation of w has to be constructed on the basis of a finite number of (inexact) measurements (observations).