Volume 1, Issue 4
Convergence Analysis of Asymptotical Regularization and Runge-Kutta Integrators for Linear Inverse Problems under Variational Source Conditions

Yubin Zhao, Peter Mathé & Shuai Lu

CSIAM Trans. Appl. Math., 1 (2020), pp. 693-714.

Published online: 2020-12

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  • Abstract

Variational source conditions are known to be a versatile tool for establishing error bounds, and these recently attract much attention. We establish sufficient conditions for general spectral regularization methods which yield convergence rates under variational source conditions. Specifically, we revisit the asymptotical regularization, Runge-Kutta integrators, and verify that these methods satisfy the proposed conditions. Numerical examples confirm the theoretical findings.

  • Keywords

Linear ill-posed problems, regularization theory, variational source conditions, asymptotical regularization, Runge-Kutta integrators.

  • AMS Subject Headings

47A52, 65J20

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COPYRIGHT: © Global Science Press

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@Article{CSIAM-AM-1-693, author = {Yubin and Zhao and and 10037 and and Yubin Zhao and Peter and Mathé and and 10038 and and Peter Mathé and Shuai and Lu and and 10039 and and Shuai Lu}, title = {Convergence Analysis of Asymptotical Regularization and Runge-Kutta Integrators for Linear Inverse Problems under Variational Source Conditions}, journal = {CSIAM Transactions on Applied Mathematics}, year = {2020}, volume = {1}, number = {4}, pages = {693--714}, abstract = {

Variational source conditions are known to be a versatile tool for establishing error bounds, and these recently attract much attention. We establish sufficient conditions for general spectral regularization methods which yield convergence rates under variational source conditions. Specifically, we revisit the asymptotical regularization, Runge-Kutta integrators, and verify that these methods satisfy the proposed conditions. Numerical examples confirm the theoretical findings.

}, issn = {2708-0579}, doi = {https://doi.org/10.4208/csiam-am.2020-0022}, url = {http://global-sci.org/intro/article_detail/csiam-am/18542.html} }
TY - JOUR T1 - Convergence Analysis of Asymptotical Regularization and Runge-Kutta Integrators for Linear Inverse Problems under Variational Source Conditions AU - Zhao , Yubin AU - Mathé , Peter AU - Lu , Shuai JO - CSIAM Transactions on Applied Mathematics VL - 4 SP - 693 EP - 714 PY - 2020 DA - 2020/12 SN - 1 DO - http://doi.org/10.4208/csiam-am.2020-0022 UR - https://global-sci.org/intro/article_detail/csiam-am/18542.html KW - Linear ill-posed problems, regularization theory, variational source conditions, asymptotical regularization, Runge-Kutta integrators. AB -

Variational source conditions are known to be a versatile tool for establishing error bounds, and these recently attract much attention. We establish sufficient conditions for general spectral regularization methods which yield convergence rates under variational source conditions. Specifically, we revisit the asymptotical regularization, Runge-Kutta integrators, and verify that these methods satisfy the proposed conditions. Numerical examples confirm the theoretical findings.

Yubin Zhao, Peter Mathé & Shuai Lu. (2020). Convergence Analysis of Asymptotical Regularization and Runge-Kutta Integrators for Linear Inverse Problems under Variational Source Conditions. CSIAM Transactions on Applied Mathematics. 1 (4). 693-714. doi:10.4208/csiam-am.2020-0022
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