Convergence Analysis of Asymptotical Regularization and Runge-Kutta Integrators for Linear Inverse Problems under Variational Source Conditions
Year: 2020
Author: Yubin Zhao, Peter Mathé, Shuai Lu
CSIAM Transactions on Applied Mathematics, Vol. 1 (2020), Iss. 4 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/csiam-am.2020-0022
CSIAM Transactions on Applied Mathematics, Vol. 1 (2020), Iss. 4 : pp. 693–714
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Linear ill-posed problems regularization theory variational source conditions asymptotical regularization Runge-Kutta integrators.