Convergence rate of runge–kutta-type regularization for nonlinear ill-posed problems under logarithmic source condition
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...
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th-mahidol.773802022-08-04T15:56:44Z Convergence rate of runge–kutta-type regularization for nonlinear ill-posed problems under logarithmic source condition Pornsarp Pornsawad Elena Resmerita Christine Böckmann Institut für Mathematik der Universität Potsdam Alfred-Wegener-Institut Helmholtz-Zentrum für Polar- und Meeresforschung Alpen-Adria-Universität Klagenfurt Silpakorn University Mahidol University Mathematics 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. 2022-08-04T08:56:44Z 2022-08-04T08:56:44Z 2021-05-01 Article Mathematics. Vol.9, No.9 (2021) 10.3390/math9091042 22277390 2-s2.0-85106178137 https://repository.li.mahidol.ac.th/handle/123456789/77380 Mahidol University SCOPUS https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85106178137&origin=inward |
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Mathematics Pornsarp Pornsawad Elena Resmerita Christine Böckmann Convergence rate of runge–kutta-type regularization for nonlinear ill-posed problems under logarithmic source condition |
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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. |
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Institut für Mathematik der Universität Potsdam |
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Institut für Mathematik der Universität Potsdam Pornsarp Pornsawad Elena Resmerita Christine Böckmann |
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Article |
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Pornsarp Pornsawad Elena Resmerita Christine Böckmann |
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Pornsarp Pornsawad |
title |
Convergence rate of runge–kutta-type regularization for nonlinear ill-posed problems under logarithmic source condition |
title_short |
Convergence rate of runge–kutta-type regularization for nonlinear ill-posed problems under logarithmic source condition |
title_full |
Convergence rate of runge–kutta-type regularization for nonlinear ill-posed problems under logarithmic source condition |
title_fullStr |
Convergence rate of runge–kutta-type regularization for nonlinear ill-posed problems under logarithmic source condition |
title_full_unstemmed |
Convergence rate of runge–kutta-type regularization for nonlinear ill-posed problems under logarithmic source condition |
title_sort |
convergence rate of runge–kutta-type regularization for nonlinear ill-posed problems under logarithmic source condition |
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2022 |
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https://repository.li.mahidol.ac.th/handle/123456789/77380 |
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