The adaptive augmented GMRES method for solving ill-posed problems

Dynamical systems method for solving linear ill-posed problems

Various versions of the Dynamical Systems Method (DSM) are proposed for solving linear ill-posed problems with bounded and unbounded operators. Convergence of the proposed methods is proved. Some new results concerning discrepancy principle for choosing regularization parameter are obtained.

A new method for solving linear ill-posed problems

In this paper, we propose a new method for solving large-scale ill-posed problems. This method is based on the Karush–Kuhn–Tucker conditions, Fisher–Burmeister function and the discrepancy principle. The main difference from the majority of existing methods for solving ill-posed problems is that, we do not need to choose a regularization parameter in advance. Experimental results show that the ...

Solving Ill-Posed Cauchy Problems by a Krylov Subspace Method

We study the numerical solution of a Cauchy problem for a self-adjoint elliptic partial differential equation uzz − Lu = 0 in three space dimensions (x, y, z) , where the domain is cylindrical in z. Cauchy data are given on the lower boundary and the boundary values on the upper boundary is sought. The problem is severely illposed. The formal solution is written as a hyperbolic cosine function ...

Gmres , L - Curves , and Discrete Ill - Posed Problems ∗

The GMRES method is a popular iterative method for the solution of large linear systems of equations with a nonsymmetric nonsingular matrix. This paper discusses application of the GMRES method to the solution of large linear systems of equations that arise from the discretization of linear ill-posed problems. These linear systems are severely ill-conditioned and are referred to as discrete ill...

Adaptive cross approximation for ill-posed problems