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

摘要

A version of the nonstationary iterated Tikhonov method was recently introduced to regularize linear inverse problems in Banach spaces [7]. In the present work we employ this method as inner iteration of the inexact Newton regularization method REGINN [14] 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.