An edition of Inverse and ill-posed problems (2011)

Inverse and ill-posed problems

theory and applications

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Cover of: Inverse and ill-posed problems by S. I. Kabanikhin
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July 1, 2019 | History
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An edition of Inverse and ill-posed problems (2011)

Inverse and ill-posed problems

theory and applications

by

  • 0 Ratings
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  • 0 Currently reading
  • 0 Have read

The text demonstrates the methods for proving the existence (if et all) and finding of inverse and ill-posed problems solutions in linear algebra, integral and operator equations, integral geometry, spectral inverse problems, and inverse scattering problems. It is given comprehensive background material for linear ill-posed problems and for coefficient inverse problems for hyperbolic, parabolic, and elliptic equations. A lot of examples for inverse problems from physics, geophysics, biology, medicine, and other areas of application of mathematics are included.

Publish Date
Publisher
De Gruyter
Language
English
Pages
475

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Previews available in: English

Subjects
Boundary value problems, Inverse problems (Differential equations), MATHEMATICS / Differential Equations / General, Improperly posed problems

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Cover of: Inverse and ill-posed problems
Inverse and ill-posed problems: theory and applications
2011, De Gruyter
electronic resource : in English
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Book Details

Table of Contents

Preface; Denotations; 1 Basic concepts and examples; 1.1 On the definition of inverse and ill-posed problems; 1.2 Examples of inverse and ill-posed problems; 2 Ill-posed problems; 2.1 Well-posed and ill-posed problems; 2.2 On stability in different spaces; 2.3 Quasi-solution. The Ivanov theorems; 2.4 The Lavrentiev method; 2.5 The Tikhonov regularization method; 2.6 Gradient methods; 2.7 An estimate of the convergence rate with respect to the objective functional; 2.8 Conditional stability estimate and strong convergence of gradient methods applied to ill-posed problems.
2.9 The pseudoinverse and the singular value decomposition of an operator3 Ill-posed problems of linear algebra; 3.1 Generalization of the concept of a solution. Pseudo-solutions; 3.2 Regularization method; 3.3 Criteria for choosing the regularization parameter; 3.4 Iterative regularization algorithms; 3.5 Singular value decomposition; 3.6 The singular value decomposition algorithm and the Godunov method; 3.7 The square root method; 3.8 Exercises; 4 Integral equations; 4.1 Fredholm integral equations of the first kind; 4.2 Regularization of linear Volterra integral equations of the first kind.
4.3 Volterra operator equations with boundedly Lipschitz-continuous kernel4.4 Local well-posedness and uniqueness on the whole; 4.5 Well-posedness in a neighborhood of the exact solution; 4.6 Regularization of nonlinear operator equations of the first kind; 5 Integral geometry; 5.1 The Radon problem; 5.2 Reconstructing a function from its spherical means; 5.3 Determining a function of a single variable from the values of its integrals. The problem of moments; 5.4 Inverse kinematic problem of seismology; 6 Inverse spectral and scattering problems.
6.1 Direct Sturm-Liouville problem on a finite interval6.2 Inverse Sturm-Liouville problems on a finite interval; 6.3 The Gelfand-Levitan method on a finite interval; 6.4 Inverse scattering problems; 6.5 Inverse scattering problems in the time domain; 7 Linear problems for hyperbolic equations; 7.1 Reconstruction of a function from its spherical means; 7.2 The Cauchy problem for a hyperbolic equation with data on a time-like surface; 7.3 The inverse thermoacoustic problem; 7.4 Linearized multidimensional inverse problem for the wave equation; 8 Linear problems for parabolic equations.
8.1 On the formulation of inverse problems for parabolic equations and their relationship with the corresponding inverse problems for hyperbolic equations8.2 Inverse problem of heat conduction with reverse time (retrospective inverse problem); 8.3 Inverse boundary-value problems and extension problems; 8.4 Interior problems and problems of determining sources; 9 Linear problems for elliptic equations; 9.1 The uniqueness theorem and a conditional stability estimate on a plane.

Edition Notes

9.2 Formulation of the initial boundary value problem for the Laplace equation in the form of an inverse problem. Reduction to an operator equation.

Includes bibliographical references and index.

Also available in print.

Description based on print version record.

Published in
Berlin
Series
Inverse and ill-posed problems series -- 55

Classifications

Library of Congress
QA378.5 .K33 2011eb

The Physical Object

Format
[electronic resource] :
Pagination
1 online resource (xv, 475 p.
Number of pages
475

ID Numbers

Open Library
OL27047186M
Internet Archive
inverseillposedp00kaba
ISBN 10
3110224011
ISBN 13
9783110224016
OCLC/WorldCat
785776523, 772845127

Source records

Internet Archive item record
Better World Books record

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