On convergence rates for the iteratively regularized Gauss-Newton method
On convergence rates for the iteratively regularized Gauss-Newton method
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DOI：
10.1093/imanum/17.3.421
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发表时间：
1997-07-01
影响因子：
2.1
通讯作者：
Scherzer, O
中科院分区：
文献类型：
--
作者：
Blaschke, B;Neubauer, A;Scherzer, O
本文证明了当非线性算子满足一定的光滑性条件时，迭代正则化Gauss-Newton方法是求解非线性不适定问题的局部收敛方法。对于扰动数据，我们提出了先验和后验停止规则，保证收敛的迭代，如果噪声水平为零。在适当的封闭性和光滑性条件下的精确解，我们获得了相同的收敛速度为线性不适定问题。
In this paper we prove that the iteratively regularized Gauss-Newton method is a locally convergent method for solving nonlinear ill-posed problems, provided the nonlinear operator satisfies a certain smoothness condition. For perturbed data we propose a priori and a posteriori stopping rules that guarantee convergence of the iterates, if the noise level goes to zero. Under appropriate closeness and smoothness conditions on the exact solution we obtain the same convergence rates as for linear ill-posed problems.