Convergence Analysis of Asymptotical Regularization and Runge-Kutta Integrators for Linear Inverse Problems under Variational Source Conditions (CSIAM Transactions on Applied Mathematics, 2020)
Variational source conditions are known to be a versatile tool for establishing error bounds, and these recently attract much attention. We establish sufficientconditions for general spectral regularization methods which yield convergence ratesunder variational source conditions. Specifically, we revisit the asymptotical regularization, Runge-Kutta integrators, and verify that these methods satisfy the proposedconditions. Numerical examples confirm the theoretical findings.
Keywords: Linear ill-posed problems; regularization theory; variational source conditions; asymptotical regularization; Runge-Kutta integrators.