Geodesic
A posteriori stopping in iteratively regularized Gauss--Newton type methods for approximating quasi-solutions of irregular operator equations
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2022), pp. 29-42

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We consider a class of iteratively regularized Gauss–Newton type methods for approximating quasi-solutions of irregular nonlinear operator equations in Hilbert spaces. We assume that the Frechet derivative of the problem operator at the desired quasi-solution has a closed range. We propose an a-posteriori stopping rule for the considered methods and get an accuracy estimate which is proportional to the error level of input data.
Keywords: nonlinear operator equation, irregular equation, ill-posed problem, Gauss–Newton method, iterative regularization, Hilbert space, closed range, a-posteriori stopping rule, accuracy estimate.
Mots-clés : quasi-solution 
@article{IVM_2022_2_a2,
     author = {M. M. Kokurin},
     title = {A posteriori stopping in iteratively regularized {Gauss--Newton} type methods for approximating quasi-solutions of irregular operator equations},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {29--42},
     publisher = {mathdoc},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2022_2_a2/}
}
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M. M. Kokurin. A posteriori stopping in iteratively regularized Gauss--Newton type methods for approximating quasi-solutions of irregular operator equations. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2022), pp. 29-42. http://geodesic.mathdoc.fr/item/IVM_2022_2_a2/