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Towards a general convergence theory for inexact Newton regularizations

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Abstract

We develop a general convergence analysis for a class of inexact Newton-type regularizations for stably solving nonlinear ill-posed problems. Each of the methods under consideration consists of two components: the outer Newton iteration and an inner regularization scheme which, applied to the linearized system, provides the update. In this paper we give a novel and unified convergence analysis which is not confined to a specific inner regularization scheme but applies to a multitude of schemes including Landweber and steepest decent iterations, iterated Tikhonov method, and method of conjugate gradients.

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Authors and Affiliations

  1. Centre de Mathématiques Appliqués (CMAP), Ecole Polytechnique, 91128, Palaiseau Cedex, France

    Armin Lechleiter

  2. Institut für Angewandte und Numerische Mathematik and Institut für Wissenschaftliches Rechnen und Mathematische Modellbildung, Universität Karlsruhe, 76128, Karlsruhe, Germany

    Andreas Rieder

Authors
  1. Armin Lechleiter
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  2. Andreas Rieder
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Correspondence to Andreas Rieder.

Additional information

Dedicated to Alfred K. Louis on the occasion of his 60th birthday.

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Lechleiter, A., Rieder, A. Towards a general convergence theory for inexact Newton regularizations. Numer. Math. 114, 521–548 (2010). https://doi.org/10.1007/s00211-009-0256-0

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  • DOI: https://doi.org/10.1007/s00211-009-0256-0

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