Convergence of Tikhonov regularization for constrained ill-posed inverse problems

Bound Constrained Regularization for Ill-Posed Problems

We consider large scale ill-conditioned linear systems arising from discretization of ill-posed problems. Regularization is imposed through an (assumed known) upper bound constraint on the solution. An iterative scheme, requiring the computation of the smallest eigenvalue and corresponding eigenvector, is used to determine the proper level of regularization. In this paper we consider several co...

The index function and Tikhonov regularization for ill-posed problems

In this paper, we study the regularizing properties of the conditional stability estimates in ill-posed problems. First, we analyze how conditional stability estimates occur, and which properties the corresponding index functions must obey. In addition, we adapt the convergence analysis for the Tikhonov regularization in Banach spaces where the difference between the approximated solution and t...

Fractional Tikhonov regularization for linear discrete ill- posed problems

Tikhonov regularization is one of the most popular methods for solving linear systems of equations or linear least-squares problems with a severely ill-conditioned matrix A. This method replaces the given problem by a penalized least-squares problem. The present paper discusses measuring the residual error (discrepancy) in Tikhonov regularization with a seminorm that uses a fractional power of ...

A Generalized Tikhonov Regularization Fornonlinear Inverse Ill - Posed Problemsmichael

Greedy Tikhonov regularization for large linear ill-posed problems

Several numerical methods for the solution of large linear ill-posed problems combine Tikhonov regularization with an iterative method based on partial Lanczos bidiagonalization of the operator. This paper discusses the determination of the regularization parameter and the dimension of the Krylov subspace for this kind of methods. A method that requires a Krylov subspace of minimal dimension is...