A Modified Asymptotical Regularization of Nonlinear Ill-Posed Problems

Pornsarp Pornsawad, Nantawan Sapsakul 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
Nantawan Sapsakul: 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, 2019, vol. 7, issue 5, 1-19

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.

Keywords: nonlinear operator; regularization; discrepancy principle; asymptotic method; optimal rate (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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