A regularization method for nonlinear ill-posed problems

Often, physically interesting functions are not directly accessible by an experiment, and must be calculated from data of an experimental accessible quantity. If this calculation requires the inversion of a Fredholm integral equation of the first kind, the determination of the physically interesting function is an ill-posed problem. In this case, linear regularization methods should be used to perform the calculations. However, in several applications the relation between the interesting function and the experimental data is given by a nonlinear integral equation. For these problems, a nonlinear regularization method is presented together with the program NLREG. The nonlinear regularization method is essentially a generalization of Tikhonov regularization to nonlinear ill-posed problems.