Convergence Rate of Runge-Kutta-Type Regularization for Nonlinear Ill-Posed Problems under Logarithmic Source Condition

Pornsarp Pornsawad, Elena Resmerita 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
Elena Resmerita: Institute of Mathematics, Alpen-Adria University of Klagenfurt, Universitätsstr. 65-67, A-9020 Klagenfurt, Austria
Christine Böckmann: Institute of Mathematics, University of Potsdam, Karl-Liebknecht-Str. 24-25, 14476 Potsdam, Germany

Mathematics, 2021, vol. 9, issue 9, 1-15

Abstract: We prove the logarithmic convergence rate of the families of usual and modified iterative Runge-Kutta methods for nonlinear ill-posed problems between Hilbert spaces under the logarithmic source condition, and numerically verify the obtained results. The iterative regularization is terminated by the a posteriori discrepancy principle.

Keywords: nonlinear inverse problem; ill-posed problem; iterative regularization; Runge-Kutta methods; logarithmic source condition; discrepancy principle; convergence rate (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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