Abstract In this paper, the local convergence of Iteratively regularized Landweber iteration method is investigated for solving non-linear inverse problems in Banach spaces. Our analysis mainly relies on the assumption that the inverse mapping satisfies the Holder stability estimate locally. We consider both noisy as well as non-noisy data in our analysis. Under the a-priori choice of stopping index for noisy data, we show that the iterates remain in a certain ball around exact solution and obtain the convergence rates. The convergence of the Iteratively regularized Landweber iterates to the exact solution is shown under certain assumptions in the case of non-noisy data and as a by-product, under different conditions, two different convergence rates are obtained.

中文翻译：

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迭代正则化 Landweber 迭代方法：通过 Hölder 稳定性进行收敛分析

摘要 本文研究了迭代正则化Landweber迭代法在求解Banach空间非线性逆问题时的局部收敛性。我们的分析主要依赖于逆映射局部满足 Holder 稳定性估计的假设。我们在分析中同时考虑噪声和非噪声数据。在噪声数据的停止索引的先验选择下，我们表明迭代保持在精确解周围的某个球中并获得收敛率。在非噪声数据的情况下，在某些假设下显示了迭代正则化 Landweber 迭代到精确解的收敛性，并且作为副产品，在不同条件下，获得了两种不同的收敛速度。