Iteratively regularized methods for irregular nonlinear operator equations with a normally solvable derivative at the solution

作者：Kokurin M Yu^*

来源：Computational Mathematics and Mathematical Physics, 2016, 56(9): 1523-1535.

DOI：10.1134/S0965542516090098

• operator equations
• irregular operator
• Hilbert space
• normally solvable operator
• Gauss-Newton methods
• iterative regularization
• termination criterion
• estimate of accuracy

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.

• 出版日期2016-9