Barbara Kaltenbacher,
"Some Newton type methods for the regularization of nonlinear ill-posed problems"
, in Inverse Problems, 1997, B. Kaltenbacher, Some Newton type methods for the regularization of nonlinear ill-posed problems, Inverse Problems 13 (1997), 729-753
Original Titel:
Some Newton type methods for the regularization of nonlinear ill-posed problems
Sprache des Titels:
Englisch
Englische Kurzfassung:
In this paper we consider a combination of Newton's method with linear Tikhonov regularization, linear Landweber iteration and truncated SVD, for regularizing an abstract, nonlinear, ill-posed operator equation. We show that under certain smoothness conditions on the nonlinear operator,
these methods converge locally. For perturbed data we propose an a priori stopping rule, that guarantees convergence of the iterates to a solution, as the noise level goes to zero. Under appropriate closeness and smoothness assumptions on the starting value and the solution, we obtain convergence rates.
Journal:
Inverse Problems
Erscheinungsjahr:
1997
Notiz zum Zitat:
B. Kaltenbacher, Some Newton type methods for the regularization of nonlinear ill-posed problems, Inverse Problems 13 (1997), 729-753