Geodesic
Iteratively regularized Gauss--Newton method for operator equations with normally solvable derivative at the solution
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2016), pp. 3-11

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We study the iteratively regularized Gauss–Newton method in a Hilbert space for solving irregular nonlinear equations with smooth operators having normally solvable derivatives at the solution. We consider both a priori and a posteriori stopping criterions for the iterations and establish accuracy estimates for resulting approximations. In the case where the a priori stopping rule is used, the accuracy of approximations arises to be proportional to the error level in input data. The latter result generalizes well-known estimates of this kind obtained for linear equations with normally solvable operators.
Keywords: operator equation, irregular operator, Hilbert space, normally solvable operator, Gauss–Newton method, iterative regularization, stopping rule, accuracy estimate. 
@article{IVM_2016_8_a0,
     author = {A. B. Bakushinskii and M. Yu. Kokurin},
     title = {Iteratively regularized {Gauss--Newton} method for operator equations with normally solvable derivative at the solution},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--11},
     publisher = {mathdoc},
     number = {8},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2016_8_a0/}
}
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A. B. Bakushinskii; M. Yu. Kokurin. Iteratively regularized Gauss--Newton method for operator equations with normally solvable derivative at the solution. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2016), pp. 3-11. http://geodesic.mathdoc.fr/item/IVM_2016_8_a0/