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An Introduction to the Mathematical Theory of Inverse Problems

, Volume 120
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Springer, 1996 - 282 pages
  

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Table des matières

Introduction and Basic Concepts
1
12 IllPosed Problems
9
13 The WorstCase Error
14
14 Problems
21
Regularization Theory for Equations of the First Kind
23
21 A General Regularization Theory
24
22 Tikhonov Regularization
37
23 Landweber Iteration
42
42 Construction of a Fundamental System
127
43 Asymptotics of the Eigenvalues and Eigenfunctions
135
44 Some Hyperbolic Problems
146
45 The Inverse Problem
154
46 A Parameter Identification Problem
160
47 Numerical Reconstruction Techniques
165
48 Problems
170
An Inverse Scattering Problem
173

24 A Numerical Example
45
25 The Discrepancy Principle of Morozov
48
26 Landwebers Iteration Method with Stopping Rule
53
27 The Conjugate Gradient Method
57
28 Problems
63
Regularization by Discretization
65
31 Projection Methods
66
32 Galerkin Methods
73
321 The Least Squares Method
76
322 The Dual Least Squares Method
78
323 The BubnovGalerkin Method for Coercive Operators
80
33 Application to Symms Integral Equation of the First Kind
85
34 Collocation Methods
94
341 Minimum Norm Collocation
95
342 Collocation of Symms Equation
99
35 Numerical Experiments for Symms Equation
107
36 The BackusGilbert Method
115
37 Problems
122
Inverse Eigenvalue Problems
125
52 The Direct Scattering Problem
177
53 Properties of the Far Field Patterns
187
54 Uniqueness of the Inverse Problem
196
55 Numerical Methods
204
551 A Simplified Newton Method
205
552 A Modified Gradient Method
209
553 The Dual Space Method
210
56 Problems
214
Basic Facts from Functional Analysis
215
A2 Orthonormal Systems
222
A3 Linear Bounded and Compact Operators
224
A4 Sobolev Spaces of Periodic Functions
232
A5 Spectral Theory for Compact Operators in Hilbert Spaces
239
A6 The Frechet Derivative
243
Proofs of the Results of Section 27
249
References
261
Index
279
Droits d'auteur

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Expressions et termes fréquents

Fréquemment cités

Page 263 - On an inverse boundary value problem. In Seminar on Numerical Analysis and its Applications to Continuum Physics (Rio de Janeiro, 1980).

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Références issues de pages Web

JSTOR: An Introduction to the Mathematical Theory of Inverse Problems.
An Introduction to the Mathematical Theory of Inverse Problems. By An- dreas Kirsch. Springer, New York, 1996. $59.95. x+282 pp., hardbound. ...
links.jstor.org/ sici?sici=0036-1445(199712)39%3A4%3C794%3AAITTMT%3E2.0.CO%3B2-E

References
References. [AS] Milton Abramowitz and Irene Stegun, handbook of Mathematical Functions,. Dover, 1965. [A] Robert Adams, Sobolev Spaces, Academic Press, ...
www.math.ubc.ca/ ~feldman/ ibook/ ib-ref.pdf

Computational Sensorics: Design & Control of Continuum Systems
S. Andreas Kirsch, An Introduction to the Mathematical Theory of Inverse Problems; D. Colton, hw Engl, ak Louis, Surveys on Solution Methods for Inverse ...
mpdc.mae.cornell.edu/ Courses/ MAE714/ mae714.html

Scattering Theory
... Scattering Theory, 2nd edition, Springer-Verlag, 1998. A. Kirsch, An Introduction to the Mathematical Theory of Inverse Problems, Springer-Verlag, 1996. ...
numathics.com/ arens/ scattering/ Scattering.html

Phys. Rev. Lett. 84, 2068 (2000): Lemm et al. - Bayesian Approach ...
[3] A. Kirsch, An Introduction to the Mathematical Theory of Inverse Problems (Springer-Verlag, New York, 1996). [4] R. Newton, Inverse Schrödinger ...
link.aps.org/ doi/ 10.1103/ PhysRevLett.84.2068

An introduction to the mathematical theory of inverse problems
An introduction to the mathematical theory of inverse problems. Purchase this Book · Purchase this Book. Source, Springer-Verlag Applied Mathematical ...
portal.acm.org/ citation.cfm?id=236740

S0101-820520070002 Computational & Applied Mathematics Mat. apl ...
... error estimate Kirsch A. An Introduction to the Mathematical Theory of Inverse Problems An Introduction to the Mathematical Theory of Inverse Problems ...
artigos.scielo.br/ S0101-820520070002.xml

The Study of EM Ill-posed Inverse Problem
An Introduction to the Mathematical Theory of Inverse Problems, Springer-Verlag, 1996. [4] Guangyan Huang, Xiaojun, Liu, Inverse Problems in Mathematics and ...
www.emfhealth.com/ seminar/ english/ 2000/ d32.htm

Geomathematics Group, TU Kaiserslautern :: Lectures
Kirsch, A.: An Introduction to the Mathematical Theory of Inverse Problems. Springer 1996. Engl, hw, Hanke, M., Neubauer, A.: Regularization of Inverse ...
www.mathematik.uni-kl.de/ ~wwwgeo/ lectures.06s.htm

ETH Zürich - Vorlesungsverzeichnis - Lerneinheit
A. Kirsch, An Introduction to the Mathematical Theory of Inverse Problems, Springer, 1996 4. cw Groetsch: Inverse Problems in the Mathematical Sciences, ...
www.vvz.ethz.ch/ Vorlesungsverzeichnis/ lerneinheitDetailPre.do?lerneinheitId=42043& semkez=2007S& lang=de

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