Regularizing properties of a truncated Newton-CG algorithm for nonlinear inverse problems

  • This paper develops truncated Newton methods as an appropriate tool for nonlinear inverse problems which are ill-posed in the sense of Hadamard. In each Newton step an approximate solution for the linearized problem is computed with the conjugate gradient method as an inner iteration. The conjugate gradient iteration is terminated when the residual has been reduced to a prescribed percentage. Under certain assumptions on the nonlinear operator it is shown that the algorithm converges and is stable if the discrepancy principle is used to terminate the outer iteration. These assumptions are fulfilled , e.g., for the inverse problem of identifying the diffusion coefficient in a parabolic differential equation from distributed data.
Author:Martin Hanke
Serie (Series number):Preprints (rote Reihe) des Fachbereich Mathematik (280)
Document Type:Report
Language of publication:English
Publication Date:2017/10/17
Year of Publication:1996
Publishing Institute:Technische Universit├Ąt Kaiserslautern
Date of the Publication (Server):2017/10/17
Number of page:16
Faculties / Organisational entities:Kaiserslautern - Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Creative Commons 4.0 - Namensnennung, nicht kommerziell, keine Bearbeitung (CC BY-NC-ND 4.0)