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Open AccessArticle

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

1
Department of Mathematics, Faculty of Science, Silpakorn University, 6 Rachamakka Nai Rd., Nakhon Pathom 73000, Thailand
2
Centre of Excellence in Mathematics, Mahidol University, Rama 6 Rd., Bangkok 10400, Thailand
3
Institut für Mathematik, Universität Potsdam, Karl-Liebknecht-Str. 24-25, D-14476 Potsdam OT Golm, Germany
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2020, 8(4), 608; https://doi.org/10.3390/math8040608
Received: 25 March 2020 / Revised: 9 April 2020 / Accepted: 10 April 2020 / Published: 16 April 2020
(This article belongs to the Special Issue Numerical Analysis: Inverse Problems – Theory and Applications)
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. View Full-Text
Keywords: nonlinear operator; regularization; modified Landweber method; discrepancy principle; logarithmic source condition nonlinear operator; regularization; modified Landweber method; discrepancy principle; logarithmic source condition
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MDPI and ACS Style

Pornsawad, P.; Sungcharoen, P.; Böckmann, C. Convergence Rate of the Modified Landweber Method for Solving Inverse Potential Problems. Mathematics 2020, 8, 608.

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