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URN: urn:nbn:de:swb:90-283341

The Approximate Inverse in Action IV: Semi-Discrete Equations in a Banach Space Setting

Schuster, Thomas; Rieder, Andreas; Schöpfer, Frank

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.


Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Publikationstyp Forschungsbericht
Jahr 2012
Sprache Englisch
Identifikator KITopen ID: 1000028334
Verlag KIT, Karlsruhe
Serie Preprint. Institut für Wissenschaftliches Rechnen und Mathematische Modellbildung, Karlsruher Institut für Technologie ; 2012,3
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