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On the approximation of high-dimensional differential equations in the hierarchical Tucker format

Arnold, Andreas; Jahnke, Tobias

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.


Volltext §
DOI: 10.5445/IR/1000029523
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Institut für Photonik und Quantenelektronik (IPQ)
Publikationstyp Forschungsbericht/Preprint
Publikationsjahr 2012
Sprache Englisch
Identifikator urn:nbn:de:swb:90-295239
KITopen-ID: 1000029523
Verlag Karlsruher Institut für Technologie (KIT)
Serie Preprint. Institut für Wissenschaftliches Rechnen und Mathematische Modellbildung, Karlsruher Institut für Technologie ; 2012,9
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