An Introduction to the Mathematical Theory...

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Sprache: Englisch

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Beschreibung

This graduate-level textbook introduces the reader to the area of inverse problems, vital to many fields including geophysical exploration, system identification, nondestructive testing, and ultrasonic tomography. It aims to expose the basic notions and difficulties encountered with ill-posed problems, analyzing basic properties of regularization methods for ill-posed problems via several simple analytical and numerical examples. The book also presents three special nonlinear inverse problems in detail: the inverse spectral problem, the inverse problem of electrical impedance tomography (EIT), and the inverse scattering problem. The corresponding direct problems are studied with respect to existence, uniqueness, and continuous dependence on parameters. Ultimately, the text discusses theoretical results as well as numerical procedures for the inverse problems, including many exercises and illustrations to complement coursework in mathematics and engineering.

This updated text includes a new chapter on the theory of nonlinear inverse problems in response to the field¿s growing popularity, as well as a new section on the interior transmission eigenvalue problem which complements the Sturm-Liouville problem and which has received great attention since the previous edition was published.

Über den Autor

Andreas Kirsch is a Professor in the Department of Mathematics at Karlsruhe Institute of Technology.

Zusammenfassung

Provides a balance of general results and particular cases

First monograph on inverse problems which contains electrical impedance tomography and the Factorization Method

Presents new and expanded sections on nonlinear theory and nonlinear inverse problems

Includes updated examples

Inhaltsverzeichnis

Introduction and Basic Concepts.- Regularization Theory for Equations of the First Kind.- Regularization by Discretization.- Nonlinear Inverse Problems.- Inverse Eigenvalue Problems.- An Inverse Problem in Electrical Impedance Tomography.- An Inverse Scattering Problem.- Basic Facts from Functional Analysis.- References.- Index.

Details

Erscheinungsjahr:	2022
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Applied Mathematical Sciences
Inhalt:	xvii 400 S. 13 s/w Illustr. 400 p. 13 illus.
ISBN-13:	9783030633455
ISBN-10:	3030633454
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Kirsch, Andreas
Auflage:	3rd ed. 2021
Hersteller:	Springer International Publishing Springer International Publishing AG Applied Mathematical Sciences
Maße:	235 x 155 x 23 mm
Von/Mit:	Andreas Kirsch
Erscheinungsdatum:	17.02.2022
Gewicht:	0,633 kg

Artikel-ID: 121133675