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An introduction to the mathematical theory of inverse problems / Andreas Kirsch.
Author
Kirsch, Andreas, 1953-
[Browse]
Format
Book
Language
English
Εdition
Third edition.
Published/Created
Cham, Switzerland : Springer, [2021]
©2021
Description
xvii, 400 pages : illustrations ; 25 cm
Availability
Available Online
Springer Nature - Springer Mathematics and Statistics eBooks 2021 English International
Copies in the Library
Location
Call Number
Status
Location Service
Notes
ReCAP - Remote Storage
QA371 .K534 2021
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Details
Subject(s)
Inverse problems (Differential equations)
[Browse]
Series
Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 120.
[More in this series]
Applied mathematical sciences, 0066-5452 ; volume 120
Bibliographic references
Includes bibliographical references (pages 377-395) and index.
Contents
Introduction and Basic Concepts
Examples of Inverse Problems
Ill-Posed Problems
The Worst-Case Error
Problems
Regularization Theory for Equations of the First Kind
A General Regularization Theory
Tikhonov Regularization
Landweber Iteration
A Numerical Example
The Discrepancy Principle of Morozov
Landweber's Iteration Method with Stopping Rule
The Conjugate Gradient Method
Regularization by Discretization
Projection Methods
Galerkin Methods
The Least Squares Method
The Dual Least Squares Method
The Bubnov-Galerkin Method for Coercive Operators
Application to Symm's Integral Equation of the First Kind
Collocation Methods
Minimum Norm Collocation
Collocation of Symm's Equation
Numerical Experiments for Symm's Equation
The Backus-Gilbert Method
Nonlinear Inverse Problems
Local Illposedness
The Nonlinear Tikhonov Regularization
Existence of Solutions and Stability
Source Conditions And Convergence Rates
A Parameter-Identification Problem
A Glimpse on Extensions to Banach Spaces
The Nonlinear Landweber Iteration
Inverse Eigenvalue Problems
Introduction
Construction of a Fundamental System
Asymptotics of the Eigenvalues and Eigenfunctions
Some Hyperbolic Problems
The Inverse Problem
A Parameter Identification Problem
Numerical Reconstruction Techniques
An Inverse Problem in Electrical Impedance Tomography
The Direct Problem and the Neumann-Dirichlet Operator
The Factorization Method
An Inverse Scattering Problem
The Direct Scattering Problem
Properties of the Far Field Patterns
Uniqueness of the Inverse Problem
The Interior Transmission Eigenvalue Problem
The Radially Symmetric Case
Discreteness And Existence in the General Case
The Inverse Spectral Problem for the Radially Symmetric Case
Numerical Methods
A Simplified Newton Method
A Modified Gradient Method
The Dual Space Method
Basic Facts from Functional Analysis
Normed Spaces and Hilbert Spaces
Orthonormal Systems
Linear Bounded and Compact Operators
Sobolev Spaces of Periodic Functions
Sobolev Spaces on the Unit Disc
Spectral Theory for Compact Operators in Hilbert Spaces
The Fréchet Derivative
Convex Analysis
Weak Topologies
Proofs of the Results of Section 2.7
Bibliography
Index.
Show 66 more Contents items
ISBN
9783030633424 ((hardcover))
303063342X ((hardcover))
OCLC
1243474111
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An introduction to the mathematical theory of inverse problems / Andreas Kirsch.
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