Abstract
In this paper we investigate the generalized Gauss–Newton method in the following form
x n+1 = ξn – θ(F′*(xn)F′(xn), τn)F′*(xn){(F(xn) – ƒδ) – F′(xn)(xn – ξn)}, x 0, ξn ∈ 𝒟 ⊂ H 1.
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.
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