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Numerical Functional Analysis and Optimization Volume 28, 2007 - Issue 11-12
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Original Articles

Range Inclusions and Approximate Source Conditions with General Benchmark Functions

Dana Düvelmeyer Department of Mathematics, Chemnitz University of Technology, Chemnitz, Germany
,
Bernd Hofmann Department of Mathematics, Chemnitz University of Technology, Chemnitz, GermanyCorrespondence[email protected]
&
Masahiro Yamamoto Graduate School of Mathematical Sciences, University of Tokyo, Tokyo, Japan
Pages 1245-1261 | Published online: 21 Dec 2007

Citations (17)

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Read on this site (4)

Jens Flemming. (2012) Solution smoothness of ill-posed equations in Hilbert spaces: four concepts and their cross connections. Applicable Analysis 91:5, pages 1029-1044.
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Bernd Hofmann & Masahiro Yamamoto. (2010) On the interplay of source conditions and variational inequalities for nonlinear ill-posed problems. Applicable Analysis 89:11, pages 1705-1727.
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Jens Flemming & Bernd Hofmann. (2010) A New Approach to Source Conditions in Regularization with General Residual Term. Numerical Functional Analysis and Optimization 31:3, pages 254-284.
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T. Hein. (2009) A unified approach for regularizing discretized linear ill‐posed problems. Mathematical Modelling and Analysis 14:4, pages 451-466.
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Articles from other publishers (13)

Daniel Gerth. (2021) A new interpretation of (Tikhonov) regularization. Inverse Problems 37:6, pages 064002.
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De-Han Chen, Bernd Hofmann & Jun Zou. (2018) Regularization and convergence for ill-posed backward evolution equations in Banach spaces. Journal of Differential Equations 265:8, pages 3533-3566.
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De-Han Chen, Bernd Hofmann & Jun Zou. (2017) Elastic-net regularization versus ℓ 1 -regularization for linear inverse problems with quasi-sparse solutions . Inverse Problems 33:1, pages 015004.
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Radu Ioan Boţ & Bernd Hofmann. (2016) Conditional stability versus ill-posedness for operator equations with monotone operators in Hilbert space. Inverse Problems 32:12, pages 125003.
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Bernd Hofmann, Barbara Kaltenbacher & Elena Resmerita. (2016) Lavrentiev's regularization method in Hilbert spaces revisited. Inverse Problems and Imaging 10:3, pages 741-764.
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Bernd Hofmann. 2015. Mathematical and Computational Modeling. Mathematical and Computational Modeling 192 221 .
Jens Flemming, Bernd Hofmann & Peter Mathé. (2011) Sharp converse results for the regularization error using distance functions. Inverse Problems 27:2, pages 025006.
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Markus Hegland & Bernd Hofmann. (2011) Errors of regularisation under range inclusions using variable Hilbert scales. Inverse Problems & Imaging 5:3, pages 619-643.
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Radu Ioan Boţ & Bernd Hofmann. (2010) An extension of the variational inequality approach for obtaining convergence rates in regularization of nonlinear ill-posed problems. Journal of Integral Equations and Applications 22:3.
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Thomas Schuster & Frank Schöpfer. (2010) Solving linear operator equations in Banach spaces non-iteratively by the method of approximate inverse. Inverse Problems 26:8, pages 085006.
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Torsten Hein & Bernd Hofmann. (2009) Approximate source conditions for nonlinear ill-posed problems—chances and limitations. Inverse Problems 25:3, pages 035003.
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Torsten Hein. (2009) Tikhonov regularization in Banach spaces—improved convergence rates results. Inverse Problems 25:3, pages 035002.
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Peter Mathé & Bernd Hofmann. (2008) Direct and inverse results in variable Hilbert scales. Journal of Approximation Theory 154:2, pages 77-89.
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