Regularization of inverse problems by the Landweber iteration

Abstract

Landweber's method is a well-known iterative technique for regularizing linear and non-linear ill-posed equations. This thesis constructs in the Hilbert space setting a Landweber iteration to solve linear ill-posed inverse problems. Combined with an a-posteriori stopping principle known as the Discrepancy Principle, we show that the Landweber method is convergent. The fundamental principle of the criteria of Picard, the singular function analysis of Schmidt and, the concept of the generalized inverse of Moore-Penrose are illustrated.