In this paper we consider the iteratively regularized Gauss-Newton method for solving nonlinear ill-posed inverse problems. Under merely Lipschitz condition, we prove that this method together with an a posteriori stopping rule defines an order optimal regularization method if the solution is regular in some suitable sense.

In this paper we consider the iteratively regularized Gauss–Newton method for solving nonlinear ill-posed inverse problems. Under merely the Lipschitz condition, we prove that this method together with an a posteriori stopping rule defines an order optimal regularization method if the solution is regular in some suitable sense.

The representation of linear operator equations in terms of wavelet bases yields a multilevel framework, which can be exploited for iterative solution. This paper describes cascadic multilevel methods that employ conjugate gradient-type methods on each level. The iterations are on each level terminated by a stopping rule based on the discrepancy principle.

A convergence rate is established for nonstationary iterated Tik-honov regularization, applied to ill-posed problems involving closed, densely deened linear operators, under general conditions on the iteration parameters. It is also shown that an order-optimal accuracy is attained when a certain a posteriori stopping rule is used to determine the iteration number.

This paper discusses a perception-based theory for a multi-variate stopping problem with a monotone rule by Yasuda et al. (1982). The problem is developed by using the perceptive analysis of the previous work(Kurano et al. (2004)). We will show a recursive equation which determines the perceptive value of its equilibrium point for the model.

For the numerical solution of the Galerkin equations associated with linear ill-posed problems that are symmetric and positive semideenite, the method of conjugate residuals is considered. An a posteriori stopping rule is introduced, and associated estimates for the approximations are provided which are order-optimal with respect to noise in the right-hand side and with respect to the discretiz...

BACKGROUND Hepatitis B e antigen (HBeAg)-negative chronic hepatitis B (CHB) is the most frequent and difficult-to-treat viral hepatitis worldwide. HBV DNA and hepatitis B surface antigen (HBsAg) serum levels, which help the early identification of non-responders to pegylated interferon (PEG-IFN), prompt more flexible individualized therapeutic strategies exploiting the benefits of both PEG-IFN ...

Research on multitasking indicates that central processing capacity is limited, resulting in a performance decrement when central processes overlap in time. A notable exception seems to be stopping responses. The main theoretical and computational accounts of stop performance assume that going and stopping do not share processing capacity. This independence assumption has been supported by many...

A new approach to the solution of optimal stopping problems for one-dimensional diffusions is developed. It arises by imbedding the stochastic problem in a linear programming problem over a space of measures. Optimizing over a smaller class of stopping rules provides a lower bound on the value of the original problem. Then the weak duality of a restricted form of the dual linear program provide...