A modified asymptotical regularization of nonlinear ill-posed problems

A modified asymptotical regularization of nonlinear ill-posed problems

© 2019 by the authors. 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...

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Main Authors: Pornsarp Pornsawad, Nantawan Sapsakul, Christine Böckmann
Other Authors: Universität Potsdam
Format: Article
Published: 2020
Subjects:
Mathematics
Online Access:https://repository.li.mahidol.ac.th/handle/123456789/51223
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Institution: Mahidol University
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spelling th-mahidol.512232020-01-27T16:13:45Z A modified asymptotical regularization of nonlinear ill-posed problems Pornsarp Pornsawad Nantawan Sapsakul Christine Böckmann Universität Potsdam Silpakorn University Mahidol University Mathematics © 2019 by the authors. 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(xδ(T))-yδ||=τδ+ for some δ+ > δ, and an appropriate source condition. We yield the optimal rate of convergence. 2020-01-27T09:13:45Z 2020-01-27T09:13:45Z 2019-05-01 Article Mathematics. Vol.7, No.5 (2019), 419 10.3390/math7050419 22277390 2-s2.0-85073671835 https://repository.li.mahidol.ac.th/handle/123456789/51223 Mahidol University SCOPUS https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85073671835&origin=inward
institution Mahidol University
building Mahidol University Library
continent Asia
country Thailand
Thailand
content_provider Mahidol University Library
collection Mahidol University Institutional Repository
topic Mathematics
spellingShingle Mathematics
Pornsarp Pornsawad
Nantawan Sapsakul
Christine Böckmann
A modified asymptotical regularization of nonlinear ill-posed problems
description © 2019 by the authors. 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(xδ(T))-yδ||=τδ+ for some δ+ > δ, and an appropriate source condition. We yield the optimal rate of convergence.
author2 Universität Potsdam
author_facet Universität Potsdam
Pornsarp Pornsawad
Nantawan Sapsakul
Christine Böckmann
format Article
author Pornsarp Pornsawad
Nantawan Sapsakul
Christine Böckmann
author_sort Pornsarp Pornsawad
title A modified asymptotical regularization of nonlinear ill-posed problems
title_short A modified asymptotical regularization of nonlinear ill-posed problems
title_full A modified asymptotical regularization of nonlinear ill-posed problems
title_fullStr A modified asymptotical regularization of nonlinear ill-posed problems
title_full_unstemmed A modified asymptotical regularization of nonlinear ill-posed problems
title_sort modified asymptotical regularization of nonlinear ill-posed problems
publishDate 2020
url https://repository.li.mahidol.ac.th/handle/123456789/51223
_version_ 1763488188665430016

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