Regularization by Discretization

In this chapter, we study a different approach to regularizing operator equations of the form Kx = y, where x and y are elements of certain function spaces. This approach is motivated by the fact that for the numerical treatment of such equations one has to discretize the continuous problem and reduce it to a finite system of (linear or nonlinear) equations. We see in this chapter that the discretization schemes themselves are regularization strategies in the sense of Chap. 2.