An Introduction to the Mathematical Theory of Inverse Problems

Andreas Kirsch (Autor)

Buch | Hardcover

XVII, 400 Seiten

2021 | 3rd ed. 2021
Springer International Publishing (Verlag)
978-3-030-63342-4 (ISBN)

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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.

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

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.

"This monograph is a thorough and insightful introduction to the mathematics of inverse problems and a solid improvement of the previous editions, which were used to educate many researchers in the field over the last two and a half decades. As such, the volume is already a classic and can be recommended without reservations to any reader interested in both the foundations and specific examples of inverse problems relevant to modern engineering and sciences." (Alexander Mamonov, SIAM Review, Vol. 65 (2), 2023)

“This monograph is a thorough and insightful introduction to the mathematics of inverse problems and a solid improvement of the previous editions, which were used to educate many researchers in the field over the last two and a half decades. As such, the volume is already a classic and can be recommended without reservations to any reader interested in both the foundations and specific examples of inverse problems relevant to modern engineering and sciences.” (Alexander Mamonov, SIAM Review, Vol. 65 (2), 2023)

Erscheinungsdatum	01.03.2021
Reihe/Serie	Applied Mathematical Sciences
Zusatzinfo	XVII, 400 p. 13 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	786 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
Schlagworte	Conjugate Gradient Method • ill-posed problems • Impedance tomography • Inverse Problems • inverse spectral problems • Landweber's method • regularization techniques • scattering theory • Tikhonov regularization
ISBN-10	3-030-63342-X / 303063342X
ISBN-13	978-3-030-63342-4 / 9783030633424
Zustand	Neuware