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

Pornsarp Pornsawad, Parada Sungcharoen and Christine Böckmann
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Pornsarp Pornsawad: Department of Mathematics, Faculty of Science, Silpakorn University, 6 Rachamakka Nai Rd., Nakhon Pathom 73000, Thailand
Parada Sungcharoen: Department of Mathematics, Faculty of Science, Silpakorn University, 6 Rachamakka Nai Rd., Nakhon Pathom 73000, Thailand
Christine Böckmann: Institut für Mathematik, Universität Potsdam, Karl-Liebknecht-Str. 24-25, D-14476 Potsdam OT Golm, Germany

Mathematics, 2020, vol. 8, issue 4, 1-22

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.

Keywords: nonlinear operator; regularization; modified Landweber method; discrepancy principle; logarithmic source condition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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