A Modified Asymptotical Regularization of Nonlinear Ill-Posed Problems

Abstract

In this paper, we investigate the continuous version of modified iterative Runge–Kutta-type methods for nonlinear inverse ill-posed problems proposed in a previous work. The convergence analysis is proved under the tangential cone condition, a modified discrepancy principle, i.e., the stopping time T is a solution of ∥ F ( x δ ( T ) ) − y δ ∥ = τ δ + for some δ + > δ , and an appropriate source condition. We yield the optimal rate of convergence.

Keywords

• nonlinear operator
• regularization
• discrepancy principle
• asymptotic method
• optimal rate