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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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An inexact Newton regularization in Banach spaces based on the nonstationary iterated Tikhonov method

Fábio Margotti
  • Department of Mathematics, Karlsruhe Institute of Technology (KIT), 76128 Karlsruhe, Germany
  • :
/ Andreas Rieder
  • Department of Mathematics, Karlsruhe Institute of Technology (KIT), 76128 Karlsruhe, Germany
  • :
Published Online: 2014-12-06 | DOI: https://doi.org/10.1515/jiip-2014-0035

Abstract

A version of the nonstationary iterated Tikhonov method was recently introduced to regularize linear inverse problems in Banach spaces [Inverse Problems 28 (2012), Article ID 104011]. In the present work we employ this method as inner iteration of the inexact Newton regularization method REGINN [Inverse Problems 15 (1999), 309–327] which stably solves nonlinear ill-posed problems. Further, we propose and analyze a Kaczmarz version of the new scheme which allows fast solution of problems which can be split into smaller subproblems. As special cases we prove strong convergence of Kaczmarz variants of the Levenberg–Marquardt and the iterated Tikhonov methods in Banach spaces.

Keywords: Inexact Newton regularization in Banach spaces; nonstationary iterated Tikhonov method; Levenberg–Marquardt scheme; Kaczmarz iteration

MSC: 65J20; 65J15


Received: 2014-05-02

Revised: 2014-08-27

Accepted: 2014-09-21

Published Online: 2014-12-06

Published in Print: 2015-08-01


Citation Information: Journal of Inverse and Ill-posed Problems. Volume 23, Issue 4, Pages 373–392, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip-2014-0035, December 2014

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