We consider a new idea for solving Tikhonov regularized discretized ill-posed problems. The optimization problem is formulated as a nonlinear least squares problems containing the Tikhonov regularization parameter λ. In order to find the size of the regularization parameter and attain good convergence in the optimization method we use the nonlinear Land a-curve. The nonlinear L-curve is a direc...

Abstract Tikhonov regularization with square-norm penalty for linear forward operators has been studied extensively in the literature. However, results on convergence theory are based technical proofs and sometimes difficult to interpret. It is also often not clear how those translate into discrete, numerical setting. In this paper we present a new strategy study properties of method example re...

This paper is concerned with the solution of large-scale linear discrete ill-posed problems. The determination of a meaningful approximate solution of these problems requires regularization. We discuss regularization by the Tikhonov method and by truncated iteration. The choice of regularization matrix in Tikhonov regularization may significantly affect the quality of the computed approximate s...

The main goal of our paper is to study the regularization problems which occur in predictive control of systems with severely ill-posed inverse model. We propose a new formulation of predictive control where the future controls are obtained as a solution of certain ill-posed inverse problem. This formulation leads to a possibility of closed loop on-line control of complex systems with ill-posed...