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 - <p style="text-align: justify;">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.</p>