Abstract In a Hilbert space, we consider a class of conditionally well-posed inverse problems for which the Hölder type estimate of conditional stability on a bounded closed and convex subset holds. We investigate a finite-dimensional version of Tikhonov’s scheme in which the discretized Tikhonov’s functional is minimized over the finite-dimensional section of the set of conditional stability. For this optimization problem, we prove that each its stationary point that is located not too far from the desired solution of the original inverse problem in reality belongs to a small neighborhood of the solution. Estimates for the diameter of this neighborhood in terms of discretization errors and error level in input data are also given.

中文翻译：

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条件适定逆问题的吉洪诺夫泛函驻点聚类

摘要 在希尔伯特空间中，我们考虑一类条件适定逆问题，对于有界闭凸子集条件稳定性的 Hölder 类型估计成立。我们研究了有限维版本的 Tikhonov 方案，其中离散化的 Tikhonov 泛函在条件稳定性集的有限维部分上被最小化。对于这个优化问题，我们证明它的每一个离原逆问题的期望解不远的驻点都属于解的一个小邻域。还给出了在离散化误差和输入数据误差水平方面对该邻域直径的估计。