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- Title
Iteratively regularized methods for irregular nonlinear operator equations with a normally solvable derivative at the solution.
- Authors
Kokurin, M.
- Abstract
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.
- Subjects
NONLINEAR operator equations; DERIVATIVES (Mathematics); GAUSS-Newton method; HILBERT space; LINEAR equations
- Publication
Computational Mathematics & Mathematical Physics, 2016, Vol 56, Issue 9, p1523
- ISSN
0965-5425
- Publication type
Article
- DOI
10.1134/S0965542516090098