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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

DOI: 10.4208/csiam-am.2020-0022

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

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CSIAM-AM-1-693, author = {Zhao , YubinMathé , Peter and Lu , Shuai}, 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.

Zhao , YubinMathé , Peter and Lu , Shuai. (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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