The purpose of this chapter is to provide a survey of our book by placing what we have to
say in a historical context. We obviously cannot give a complete account of inverse …

Regularization methods aimed at finding stable approximate solutions are a necessary tool
to tackle inverse and ill-posed problems. Inverse problems arise in a large variety of …

The authors consider non-linear ill-posed problems in a Hilbert space setting, they show that
Tikhonov regularisation is a stable method for solving non-linear ill-posed problems and …

The first part of this paper studies a Levenberg-Marquardt scheme for nonlinear inverse
problems where the corresponding Lagrange (or regularization) parameter is chosen from …

The authors propose an a-posteriors strategy for choosing the regularization parameter in
Tikhonov regularization for solving nonlinear ill-posed problems and show that under certain …

The author studies Tikhonov regularisation as a stable method for approximating the
solutions of non-linear ill-posed problems. The authors gives conditions that guarantee the …

In this paper a new technique for the estimation of parameters in elliptic partial differential
equations is developed. It is a hybrid method combining the output-least-squares and the …

In this paper error estimates for non-quadratic regularization of nonlinear ill-posed problems
in Banach spaces are derived. Our analysis is based on a few novel features: in comparison …

The solution of an elliptic boundary value problem is an infinitely differentiable function of
the coefficient in the partial differential equation. When the (coefficient-dependent) energy …

The paper is concerned with the solution of nonlinear ill-posed problems by methods that
utilize the second derivative. A general predictor-corrector approach is developed; one …