On Steepest-Descent-Kaczmarz Methods for Regularizing Systems of Nonlinear Ill-posed Equations
Numerical Analysis
2008-08-03 v3
Abstract
We investigate modified steepest descent methods coupled with a loping Kaczmarz strategy for obtaining stable solutions of nonlinear systems of ill-posed operator equations. We show that the proposed method is a convergent regularization method. Numerical tests are presented for a linear problem related to photoacoustic tomography and a non-linear problem related to the testing of semiconductor devices.
Cite
@article{arxiv.0801.3088,
title = {On Steepest-Descent-Kaczmarz Methods for Regularizing Systems of Nonlinear Ill-posed Equations},
author = {A. De Cezaro and M. Haltmeier and A. Leitao and O. Scherzer},
journal= {arXiv preprint arXiv:0801.3088},
year = {2008}
}
Comments
22 pages (8 figures). For this version we have corrected some typos and also have corrected Equation (25) in the proof of Theorem 3.3