Abstract In this paper, we consider a simplified iteratively regularized Gauss–Newton method in a Banach space setting under a general source condition. We will obtain order-optimal error estimates both for an a priori stopping rule and for a Morozov-type stopping rule together with a posteriori choice of the regularization parameter. An advantage of a general source condition is that it provides a unified setting for the error analysis which can be applied to the cases of both severely and mildly ill-posed problems. We will give a numerical example of a parameter identification problem to discuss the performance of the method.

中文翻译：

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一般源条件下巴拿赫空间中的简化迭代正则化高斯-牛顿法

摘要 在本文中，我们在一般源条件下，在 Banach 空间设置中考虑了一种简化的迭代正则化高斯-牛顿方法。我们将获得先验停止规则和 Morozov 型停止规则的阶次最优误差估计以及正则化参数的后验选择。一般源条件的一个优点是它为误差分析提供了统一的设置，可以应用于严重和轻度不适定问题的情况。我们将给出一个参数识别问题的数值例子来讨论该方法的性能。