Continuous regularized Gauss-Newton-type algorithm for nonlinear ill-posed equations with simultaneous updates of inverse derivative
نویسندگان
چکیده
A new continuous regularized Gauss-Newton-type method with simultaneous updates of the operator (F (x(t))F (x(t)) + ε(t)I) for solving nonlinear ill-posed equations in a Hilbert space is proposed. A convergence theorem is proved. An attractive and novel feature of the proposed method is the absence of the assumptions about the location of the spectrum of the operator F (x). The absence of such assumptions is made possible by a source-type condition.
منابع مشابه
A convergence analysis of the iteratively regularized Gauss--Newton method under the Lipschitz condition
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.
متن کاملA convergence analysis of the iteratively regularized Gauss-Newton method under Lipschitz condition
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.
متن کاملConvergence rates of the continuous regularized Gauss—Newton method
In this paper a convergence proof is given for the continuous analog of the Gauss—Newton method for nonlinear ill-posed operator equations and convergence rates are obtained. Convergence for exact data is proved for nonmonotone operators under weaker source conditions than before. Moreover, nonlinear ill-posed problems with noisy data are considered and a priori and a posteriori stopping rules ...
متن کاملNewton-type regularization methods for nonlinear inverse problems
Inverse problems arise whenever one searches for unknown causes based on observation of their effects. Such problems are usually ill-posed in the sense that their solutions do not depend continuously on the data. In practical applications, one never has the exact data; instead only noisy data are available due to errors in the measurements. Thus, the development of stable methods for solving in...
متن کاملConvergence and Application of a Modified Iteratively Regularized Gauss-Newton Algorithm
We establish theoretical convergence results for an Iteratively Regularized Gauss Newton (IRGN) algorithm with a specific Tikhonov regularization. This Tikhnov regularization, which uses a seminorm generated by a linear operator, is motivated by mapping of the minimization variables to physical space which exposes the different scales of the parameters and therefore also suggests appropriate we...
متن کامل