Geodesic
Stable approximation of solutions to irregular nonlinear operator equations in a Hilbert space under large noise
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 1, pp. 3-10 Cet article a éte moissonné depuis la source Math-Net.Ru

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The class of regularized Gauss–Newton methods for solving inexactly specified irregular nonlinear equations is examined under the condition that additive perturbations of the operator in the problem are close to zero only in the weak topology. By analogy with the well-understood conventional situation where the perturbed and exact operators are close in norm, a stopping criterion is constructed ensuring that the approximate solution is adequate to the errors in the operator. 
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M. Yu. Kokurin. Stable approximation of solutions to irregular nonlinear operator equations in a Hilbert space under large noise. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 1, pp. 3-10. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_1_a0/

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