Geodesic
Iteratively regularized methods for irregular nonlinear operator equations with a normally solvable derivative at the solution
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 9, pp. 1543-1555 Cet article a éte moissonné depuis la source Math-Net.Ru

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A group of iteratively regularized methods of Gauss–Newton type for solving irregular nonlinear equations with smooth operators in a Hilbert space under the condition of normal solvability of the derivative of the operator at the solution is considered. A priori and a posteriori methods for termination of iterations are studied, and estimates of the accuracy of approximations obtained are found. It is shown that, in the case of a priori termination, the accuracy of the approximation is proportional to the error in the input data. Under certain additional conditions, the same estimate is established for a posterior termination from the residual principle. These results generalize known similar estimates for linear equations with a normally solvable operator. 
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M. Yu. Kokurin. Iteratively regularized methods for irregular nonlinear operator equations with a normally solvable derivative at the solution. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 9, pp. 1543-1555. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_9_a0/

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