BÜCHER VERSANDKOSTENFREI INNERHALB DEUTSCHLANDS
eBook
Variational Source Conditions, Quadratic Inverse Problems, Sparsity Promoting Regularization
New Results in Modern Theory of Inverse Problems and an Application in Laser Optics
Springer International Publishing
ISBN 978-3-319-95264-2
Standardpreis
Bibliografische Daten
eBook. PDF. Weiches DRM (Wasserzeichen)
2018
XI, 182 p. 35 illus..
In englischer Sprache
Umfang: 182 S.
Verlag: Springer International Publishing
ISBN: 978-3-319-95264-2
Weiterführende bibliografische Daten
Das Werk ist Teil der Reihe: Frontiers in Mathematics
Produktbeschreibung
The book collects and contributes new results on the theory and practice of ill-posed inverse problems.
Different notions of ill-posedness in Banach spaces for linear and nonlinear inverse problems are discussed not only in standard settings but also in situations up to now not covered by the literature. Especially, ill-posedness of linear operators with uncomplemented null spaces is examined.
Tools for convergence rate analysis of regularization methods are extended to a wider field of applicability. It is shown that the tool known as variational source condition always yields convergence rate results.
A theory for nonlinear inverse problems with quadratic structure is developed as well as corresponding regularization methods. The new methods are applied to a difficult inverse problem from laser optics.
Sparsity promoting regularization is examined in detail from a Banach space point of view. Extensive convergence analysis reveals new insights into the behavior of Tikhonov-type regularization with sparsity enforcing penalty.
Autorinnen und Autoren
Produktsicherheit
Hersteller
Springer Nature Customer Service Center GmbH
ProductSafety@springernature.com
Rezensionen
