A new approach to convergence rate analysis of Tikhonov regularization for parameter identification in heat conduction
A new approach to convergence rate analysis of Tikhonov regularization for parameter identification in heat conduction
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DOI：
10.1088/0266-5611/16/6/319
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发表时间：
2000
期刊：
影响因子：
2.1
通讯作者：
Heinz W Engl;Jun Zou
中科院分区：
文献类型：
--
作者：
Heinz W Engl;Jun Zou
本文研究了广泛使用的带Tikhonov正则化的输出最小二乘方法在热传导系统中电导率分布辨识中的稳定性和收敛速度。由于所涉及的非线性参数-解算子的源条件和正则性假设相当严格，现有的非线性逆问题的Tikhonov正则化理论难以应用于本文的收敛速率分析。通过引入一些新技术，我们能够放松这些正则性要求，并推导出一个更简单和易于解释的源条件，但仍然达到与标准Tikhonov正则化理论相同的收敛速率。
In this paper we investigate the stability and convergence rates of the widely used output least-squares method with Tikhonov regularization for the identification of the conductivity distribution in a heat conduction system. Due to the rather restrictive source conditions and regularity assumptions on the nonlinear parameter-to-solution operator concerned, the existing Tikhonov regularization theory for nonlinear inverse problems is difficult to apply for the convergence rate analysis here. By introducing some new techniques, we are able to relax these regularity requirements and derive a much simpler and easily interpretable source condition but still achieve the same convergence rates as the standard Tikhonov regularization theory does.