Convergence Analysis of Asymptotical Regularization and Runge-Kutta Integrators for Linear Inverse Problems under Variational Source Conditions

Abstract

Variational source conditions are known to be a versatile tool for establish-ing 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 regular-ization, 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