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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)



Further convergence results on the general iteratively regularized Gauss-Newton methods under the discrepancy principle

Author: Qinian Jin
Journal: Math. Comp. 82 (2013), 1647-1665
MSC (2010): Primary 65J15, 65J20; Secondary 65H17
Published electronically: December 31, 2012
MathSciNet review: 3042580
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Abstract: We consider the general iteratively regularized Gauss-Newton

$\displaystyle x_{k+1}^\delta =x_0-g_{\alpha _k}(F'(x_k^\delta )^*F'(x_k^\delta ... ...a )^* \left (F(x_k^\delta )-y^\delta -F'(x_k^\delta )(x_k^\delta -x_0)\right ) $

for solving nonlinear inverse problems $ F(x)=y$ using the only available noise $ y^\delta $ of $ y$ satisfying $ \Vert y^\delta -y\Vert\le \delta $ with a given small noise level $ \delta >0$. In order to produce reasonable approximation to the sought solution, we terminate the iteration by the discrepancy principle. Under much weaker conditions we derive some further convergence results which improve the existing ones and thus expand the applied range.

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Additional Information

Qinian Jin
Affiliation: Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061
Address at time of publication: Mathematical Sciences Institute, The Australian National University, Canberra, ACT 0200, Australia

Keywords: Nonlinear inverse problems, the general iteratively regularized Gauss-Newton methods, the discrepancy principle, convergence, order optimality
Received by editor(s): June 30, 2010
Received by editor(s) in revised form: August 22, 2011
Published electronically: December 31, 2012
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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