On generalized iterated Tikhonov regularization with operator-dependent seminorms

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Electronic Transactions on Numerical Analysis Pub Date : 2018-01-01 DOI:10.1553/ETNA_VOL47S73

D. Bianchi, M. Donatelli

引用次数: 14

Abstract

We investigate the recently introduced Tikhonov regularization filters with penalty terms having seminorms that depend on the operator itself. Exploiting the singular value decomposition of the operator, we provide optimal order conditions, smoothing properties, and a general condition (with a minor condition of the seminorm) for the saturation level. Moreover, we introduce and analyze both stationary and nonstationary iterative counterparts of the generalized Tikhonov method with operator-dependent seminorms. We establish their convergence rate under conditions affecting only the iteration parameters, proving that they overcome the saturation result. Finally, some selected numerical results confirm the effectiveness of the proposed regularization filters.

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算子相关半模的广义迭代Tikhonov正则化

我们研究了最近引入的吉洪诺夫正则化滤波器，其惩罚项具有依赖于算子本身的半正规。利用算子的奇异值分解，我们提供了饱和水平的最优阶条件、平滑性质和一般条件(含半正规的次要条件)。此外，我们还引入并分析了具有算子相关半模的广义Tikhonov方法的平稳迭代对应物和非平稳迭代对应物。在只影响迭代参数的条件下，建立了它们的收敛速度，证明了它们克服了饱和结果。最后，选定的一些数值结果验证了所提正则化滤波器的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Electronic Transactions on Numerical Analysis 数学-应用数学

CiteScore

2.10

自引率

7.70%

发文量

审稿时长

6 months

期刊介绍： Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM).