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

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    Details

    Subject(s)
    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.
    ISBN
    • 9783030633424 ((hardcover))
    • 303063342X ((hardcover))
    OCLC
    1243474111
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