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Discrepancy principle for generalized GN iterations combined with the reverse connection control
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Anatoly Bakushinsky
Published/Copyright:
October 20, 2010
Abstract
In this paper we investigate the generalized Gauss–Newton method in the following form
xn+1 = ξn – θ(F′*(xn)F′(xn), τn)F′*(xn){(F(xn) – ƒδ) – F′(xn)(xn – ξn)}, x0, ξn ∈ 𝒟 ⊂ H1.
The modified source condition
which depends on the current iteration point xn, is used. We call this inclusion the undetermined reverse connection. The new source condition leads to a much larger set of admissible control elements ξn as compared to the previously studied versions, where ξn = ξ. The process is combined with a novel a posteriori stopping rule, where 
is the number of the first transition of ‖F(xn) – ƒδ‖ through the given level δω, 0, < ω < 1, i.e.,
The convergence analysis of the proposed algorithm is given.
Keywords.: Stopping rule; discrepancy principle; ill-posed problem; iterative regularization; Fréchet derivative; Gauss–Newton's method
Received: 2010-04-01
Published Online: 2010-10-20
Published in Print: 2010-October
© de Gruyter 2010
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Keywords for this article
Stopping rule;
discrepancy principle;
ill-posed problem;
iterative regularization;
Fréchet derivative;
Gauss–Newton's method
Articles in the same Issue
- An inverse nodal problem for integro-differential operators
- Reconstruction of pressure velocities and boundaries of thin layers in thinly-stratified layers
- Restoration of tape matrices with the help of the spectral date
- On the inversion formulas of Pestov and Uhlmann for the geodesic ray transform
- On regularization method for numerical inversion of the Laplace transforms computable at any point on the real axis
- Discrepancy principle for generalized GN iterations combined with the reverse connection control
- Recovering memory kernels in parabolic transmission problems in infinite time intervals: the non-accessible case
