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Applicable Analysis
An International Journal
Volume 88, 2009 - Issue 5: Inverse Problems
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Original Articles

On Tikhonov regularization in Banach spaces – optimal convergence rates results

Torsten Hein Faculty of Mathematics, TU Chemnitz, Chemnitz, GermanyCorrespondence[email protected]
Pages 653-667 | Received 11 Jul 2008, Accepted 04 Oct 2008, Published online: 22 Jul 2009

References

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  • Engl , HW , Hanke , M and Neubauer , A . 1996 . Regularization of Inverse Problems , Dortrecht : Kluwer Academic Publishers .
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  • Schöpfer , F , Louis , AK and Schuster , T . 2006 . Nonlinear iterative methods for linear ill-posed problems in Banach spaces . Inverse Probl. , 22 : 311 – 329 .
  • Hein , T . Regularization of ill-posed problems in Banach spaces - approximative source conditions and convergence rates results , TU Chemnitz, Faculty of Mathematics . (Accepted for publication), Preprint 2007-28
  • Engl , HW , Kunisch , K and Neubauer , A . 1989 . Convergence rates for Tikhonov regularization of non-linear ill-posed problems . Inverse Probl. , 5 : 523 – 540 .
  • Seidman , TI and Vogel , CR . 1989 . Well posedness and convergence of some regularisation methods for non-linear ill-posed problems . Inverse Probl. , 5 : 227 – 238 .
  • Cioranescu , I . 1990 . Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems , Dortrecht : Kluwer Academic Publishers .
  • Xu , Z-B and Roach , GF . 1991 . Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces . J. Math. Anal. Appl , 157 : 189 – 210 .
  • Lepskij , OV . 1990 . A problem of adaptive estimation in Gaussian white noise . Teor. Veroyatn. Primen , 35 : 459 – 470 .
  • Mathé , P . 2006 . The Lepskij principle revisited . Inverse Probl. , 22 : L11 – L15 .
  • Bauer , F and Hohage , T . 2005 . A Lepskij-type stopping rule for regularized Newton methods . Inverse Probl. , 21 : 1979 – 1991 .

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