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A Modified Asymptotical Regularization of Nonlinear Ill-Posed Problems

Author

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  • Pornsarp Pornsawad

    (Department of Mathematics, Faculty of Science, Silpakorn University, 6 Rachamakka Nai Rd., Nakhon Pathom 73000, Thailand
    Centre of Excellence in Mathematics, Mahidol University, Rama 6 Rd., Bangkok 10400, Thailand)

  • Nantawan Sapsakul

    (Department of Mathematics, Faculty of Science, Silpakorn University, 6 Rachamakka Nai Rd., Nakhon Pathom 73000, Thailand
    Centre of Excellence in Mathematics, Mahidol University, Rama 6 Rd., Bangkok 10400, Thailand)

  • Christine Böckmann

    (Institut für Mathematik, Universität Potsdam, Karl-Liebknecht-Str. 24-25, D-14476 Potsdam OT Golm, Germany)

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.

Suggested Citation

  • Pornsarp Pornsawad & Nantawan Sapsakul & Christine Böckmann, 2019. "A Modified Asymptotical Regularization of Nonlinear Ill-Posed Problems," Mathematics, MDPI, vol. 7(5), pages 1-19, May.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:5:p:419-:d:230073
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    Citations

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    Cited by:

    1. Pornsarp Pornsawad & Elena Resmerita & Christine Böckmann, 2021. "Convergence Rate of Runge-Kutta-Type Regularization for Nonlinear Ill-Posed Problems under Logarithmic Source Condition," Mathematics, MDPI, vol. 9(9), pages 1-15, May.
    2. Pornsarp Pornsawad & Parada Sungcharoen & Christine Böckmann, 2020. "Convergence Rate of the Modified Landweber Method for Solving Inverse Potential Problems," Mathematics, MDPI, vol. 8(4), pages 1-22, April.

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