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An introduction to the mathematical ...

Kirsch, Andreas.

An introduction to the mathematical theory of inverse problems

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	An introduction to the mathematical theory of inverse problemsby Andreas Kirsch.
作者:	Kirsch, Andreas.
出版者:	Cham :Springer International Publishing :2021.
面頁冊數:	xvii, 400 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Inverse problems (Differential equations)
電子資源:	https://doi.org/10.1007/978-3-030-63343-1
ISBN:	9783030633431$q(electronic bk.)

An introduction to the mathematical theory of inverse problems
Kirsch, Andreas.

An introduction to the mathematical theory of inverse problems[electronic resource] /by Andreas Kirsch. - Third edition. - Cham :Springer International Publishing :2021. - xvii, 400 p. :ill., digital ;24 cm. - Applied mathematical sciences,v.1200066-5452 ;. - Applied mathematical sciences ;v.176..

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 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.

ISBN: 9783030633431$q(electronic bk.)

Standard No.: 10.1007/978-3-030-63343-1doiSubjects--Topical Terms:

189581
Inverse problems (Differential equations)

LC Class. No.: QA371

Dewey Class. No.: 515.357

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520 $a 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.
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