Mathematics (May 2019)

A Modified Asymptotical Regularization of Nonlinear Ill-Posed Problems

  • Pornsarp Pornsawad,
  • Nantawan Sapsakul,
  • Christine Böckmann

DOI
https://doi.org/10.3390/math7050419
Journal volume & issue
Vol. 7, no. 5
p. 419

Abstract

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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