Abstract

Ill posed problems constitute the mathematical model of a large variety of applications. Aim of this paper is to define an iterative algorithm finding the solution of a regularization problem. The method minimizes a function constituted by a least squares term and a generally nonlinear regularization term, weighted by a regularization parameter. The proposed method computes a sequence of iterates approximating the regularization parameter and a sequence of iterates approximating the solution. The numerical experiments performed on 1D test problems show that the algorithm gives good results with different regularization functions both in terms of precision and computational efficiency. Moreover, it could be easily applied to large size regularization problems.