On the regularization of nonlinear ill-posed problems via inexact Newton iterations
On the regularization of nonlinear ill-posed problems via inexact Newton iterations
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DOI：
10.1088/0266-5611/15/1/028
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发表时间：
1999-02
期刊：
影响因子：
2.1
通讯作者：
A. Rieder
中科院分区：
文献类型：
--
作者：
A. Rieder
研究了求解非线性不适定问题稳定解的不精确牛顿方法。相应的内部格式可以选择为具有足够收敛模数的任何线性正则化。验证了这些牛顿型算法的正则化性质，即当噪声水平趋于零时，迭代收敛到具有精确数据的非线性问题的解。此外，还给出了收敛速度。最后，讨论了算法的实现问题，并将该算法应用于一个椭圆型偏微分方程组的参数辨识问题。数值结果很好地再现了理论预测，表明了该方法的有效性。
Inexact Newton methods for the stable solution of nonlinear ill-posed problems are considered. The corresponding inner scheme can be chosen to be any linear regularization with a sufficient modulus of convergence. The regularization property of these Newton-type algorithms is verified, that is, the iterates converge to a solution of the nonlinear problem with exact data when the noise level tends to zero. Moreover, convergence rates are given. Finally, implementation issues are discussed and the algorithm is applied to a parameter identification problem for an elliptic PDE. The numerical results reproduce nicely theoretical predictions and show the efficiency of the proposed method.