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Volltext preprint nr. 12-09.pdf1.pdf (1,0 MB)
URN (für Zitat) http://nbn-resolving.org/urn:nbn:de:swb:90-295239
Titel On the approximation of high-dimensional differential equations in the hierarchical Tucker format
Autor Arnold, Andreas
Jahnke, Tobias
Institution Fakultät für Elektrotechnik und Informationstechnik (ETIT)
Fakultät für Mathematik (MATH)
Institut für Angewandte und Numerische Mathematik (IANM)
Institut für Photonik und Quantenelektronik (IPQ)
Dokumenttyp Buch
Verlag KIT, Karlsruhe
Jahr 2012
Serie Preprint. Institut für Wissenschaftliches Rechnen und Mathematische Modellbildung, Karlsruher Institut für Technologie ; 2012,9
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.