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Convergence Rate of the Modified Landweber Method for Solving Inverse Potential Problems

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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
    These authors contributed equally to this work.)

  • Parada Sungcharoen

    (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
    These authors contributed equally to this work.)

  • Christine Böckmann

    (Institut für Mathematik, Universität Potsdam, Karl-Liebknecht-Str. 24-25, D-14476 Potsdam OT Golm, Germany
    These authors contributed equally to this work.)

Abstract

In this paper, we present the convergence rate analysis of the modified Landweber method under logarithmic source condition for nonlinear ill-posed problems. The regularization parameter is chosen according to the discrepancy principle. The reconstructions of the shape of an unknown domain for an inverse potential problem by using the modified Landweber method are exhibited.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:608-:d:346180
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    References listed on IDEAS

    as
    1. 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.
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