
doi: 10.1007/bf01385697
Iterated Tikhonov regularization for the solution of nonlinear ill-posed problems is investigated. In the case of linear ill-posed problems it is well-known that (under appropriate assumptions) the \(n\)-th iterated regularized solutions can converge like \(O(\delta^{{2n \over 2n+1}})\), where \(\delta\) denotes the noise level of the data perturbation. Conditions are given that guarantee this convergence rate also for nonlinear ill-posed problems, and these conditions are motivated by the mapping degree. The results are derived by a comparison of the iterated regularized solutions of the nonlinear problem with the iterated regularized solutions of its linearization. Numerical examples are presented.
numerical examples, parameter identification, convergence rate, 510.mathematics, Numerical solutions of ill-posed problems in abstract spaces; regularization, Iterative procedures involving nonlinear operators, inverse problems, Numerical solutions to equations with nonlinear operators, nonlinear ill-posed problems, Article, iterated Tikhonov regularization
numerical examples, parameter identification, convergence rate, 510.mathematics, Numerical solutions of ill-posed problems in abstract spaces; regularization, Iterative procedures involving nonlinear operators, inverse problems, Numerical solutions to equations with nonlinear operators, nonlinear ill-posed problems, Article, iterated Tikhonov regularization
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