عنوان
پدید آورنده
موضوع
رده
QA378.5 .N355 2015eb
QA378
.
5
.
N355
2015eb
کتابخانه
محل استقرار
INTERNATIONAL STANDARD BOOK NUMBER
(Number (ISBN
0750312181
(Number (ISBN
0750312203
(Number (ISBN
9780750312189
(Number (ISBN
9780750312202
Erroneous ISBN
9780750312196
TITLE AND STATEMENT OF RESPONSIBILITY
Title Proper
Inverse modeling :
General Material Designation
[Book]
Other Title Information
an introduction to the theory and methods of inverse problems and data assimilation /
First Statement of Responsibility
Gen Nakamura and Roland Potthast.
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) :
Name of Publisher, Distributor, etc.
IOP Publishing,
Date of Publication, Distribution, etc.
[2015]
PHYSICAL DESCRIPTION
Specific Material Designation and Extent of Item
1 online resource (various pagings) :
Other Physical Details
illustrations (some color).
SERIES
Series Title
IOP expanding physics,
ISSN of Series
2053-2563
GENERAL NOTES
Text of Note
"Version: 20151201"--Title page verso.
Text of Note
Title from PDF title page (viewed on January 10, 2016).
INTERNAL BIBLIOGRAPHIES/INDEXES NOTE
Text of Note
Includes bibliographical references.
CONTENTS NOTE
Text of Note
Preface -- 1. Introduction -- 1.1. A tour through theory and applications -- 1.2. Types of inverse problems.
Text of Note
10. Analysis : uniqueness, stability and convergence questions -- 10.1. Uniqueness of inverse problems -- 10.2. Uniqueness and stability for inverse obstacle scattering -- 10.3. Discrete versus continuous problems -- 10.4. Relation between inverse scattering and inverse boundary value problems -- 10.5. Stability of cycled data assimilation -- 10.6. Review of convergence concepts for inverse problems.
Text of Note
11. Source reconstruction and magnetic tomography -- 11.1. Current simulation -- 11.2. The Biot-Savart operator and magnetic tomography -- 11.3. Parameter estimation in dynamic magnetic tomography -- 11.4. Classification methods for inverse problems.
Text of Note
12. Field reconstruction techniques -- 12.1. Series expansion methods -- 12.2. Fourier plane-wave methods -- 12.3. The potential or Kirsch-Kress method -- 12.4. The point source method -- 12.5. Duality and equivalence for the potential method and the point source method.
Text of Note
13. Sampling methods -- 13.1. Orthogonality or direct sampling -- 13.2. The linear sampling method of Colton and Kirsch -- 13.3. Kirsch's factorization method.
Text of Note
14. Probe methods -- 14.1. The SSM -- 14.2. The probing method for near field data by Ikehata -- 14.3. The multi-wave no-response and range test of Schulz and Potthast -- 14.4. Equivalence results -- 14.5. The multi-wave enclosure method of Ikehata.
Text of Note
15. Analytic continuation tests -- 15.1. The range test -- 15.2. The no-response test of Luke-Potthast -- 15.3. Duality and equivalence for the range test and no-response test -- 15.4. Ikehata's enclosure method.
Text of Note
16. Dynamical sampling and probe methods -- 16.1. Linear sampling method for identifying cavities in a heat conductor -- 16.2. Nakamura's dynamical probe method -- 16.3. The time-domain probe method -- 16.4. The BC method of Belishev for the wave equation.
Text of Note
17. Targeted observations and meta-inverse problems -- 17.1. A framework for meta-inverse problems -- 17.2. Framework adaption or zoom -- 17.3. Inverse source problems -- Appendix A.
Text of Note
2. Functional analytic tools -- 2.1. Normed spaces, elementary topology and compactness -- 2.2. Hilbert spaces, orthogonal systems and Fourier expansion -- 2.3. Bounded operators, Neumann series and compactness -- 2.4. Adjoint operators, eigenvalues and singular values -- 2.5. Lax-Milgram and weak solutions to boundary value problems -- 2.6. The Fréchet derivative and calculus in normed spaces.
Text of Note
3. Approaches to regularization -- 3.1. Classical regularization methods -- 3.2. The Moore-Penrose pseudo-inverse and Tikhonov regularization -- 3.3. Iterative approaches to inverse problems.
Text of Note
4. A stochastic view of inverse problems -- 4.1. Stochastic estimators based on ensembles and particles -- 4.2. Bayesian methods -- 4.3. Markov chain Monte Carlo methods -- 4.4. Metropolis-Hastings and Gibbs sampler -- 4.5. Basic stochastic concepts.
Text of Note
5. Dynamical systems inversion and data assimilation -- 5.1. Set-up for data assimilation -- 5.2. Three-dimensional variational data assimilation (3D-VAR) -- 5.3. Four-dimensional variational data assimilation (4D-VAR) -- 5.4. The Kalman filter and Kalman smoother -- 5.5. Ensemble Kalman filters (EnKFs) -- 5.6. Particle filters and nonlinear Bayesian data assimilation.
Text of Note
6. Programming of numerical algorithms and useful tools -- 6.1. MATLAB or OCTAVE programming : the butterfly -- 6.2. Data assimilation made simple -- 6.3. Ensemble data assimilation in a nutshell -- 6.4. An integral equation of the first kind, regularization and atmospheric radiance retrievals -- 6.5. Integro-differential equations and neural fields -- 6.6. Image processing operators.
Text of Note
7. Neural field inversion and kernel reconstruction -- 7.1. Simulating neural fields -- 7.2. Integral kernel reconstruction -- 7.3. A collocation method for kernel reconstruction -- 7.4. Traveling neural pulses and homogeneous kernels -- 7.5. Bi-orthogonal basis functions and integral operator inversion -- 7.6. Dimensional reduction and localization.
Text of Note
8. Simulation of waves and fields -- 8.1. Potentials and potential operators -- 8.2. Simulation of wave scattering -- 8.3. The far field and the far field operator -- 8.4. Reciprocity relations -- 8.5. The Lax-Phillips method to calculate scattered waves.
Text of Note
9. Nonlinear operators -- 9.1. Domain derivatives for boundary integral operators -- 9.2. Domain derivatives for boundary value problems -- 9.3. Alternative approaches to domain derivatives -- 9.4. Gradient and Newton methods for inverse scattering -- 9.5. Differentiating dynamical systems : tangent linear models.
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SUMMARY OR ABSTRACT
Text of Note
This book provides a comprehensive introduction to the techniques, tools and methods for inverse problems and data assimilation, and is written at the interface between mathematics and applications for students, researchers and developers in mathematics, physics, engineering, acoustics, electromagnetics, meteorology, biology, environmental and other applied sciences. Basic analytic questions and tools are introduced, as well as a wide variety of concepts, methods and approaches to formulate and solve inverse problems. OCTAVE /MATLAB codes are included, which serve as a first step towards simulations and more sophisticated inversion or data assimilation algorithms.
OTHER EDITION IN ANOTHER MEDIUM
International Standard Book Number
9780750312196
PARALLEL TITLE PROPER
Parallel Title
Introduction to the theory and methods of inverse problems and data assimilation
TOPICAL NAME USED AS SUBJECT
Inverse problems (Differential equations)
Stochastic processes.
Applied mathematics.
Inverse problems (Differential equations)
MATHEMATICS-- Applied.
Stochastic processes.
(SUBJECT CATEGORY (Provisional
MAT003000
PBW
DEWEY DECIMAL CLASSIFICATION
Number
511/
.
8
Edition
23
LIBRARY OF CONGRESS CLASSIFICATION
Class number
QA378
.
5
Book number
.
N355
2015eb
PERSONAL NAME - PRIMARY RESPONSIBILITY
Nakamura, Gen, (Professor of mathematics)
PERSONAL NAME - ALTERNATIVE RESPONSIBILITY
Potthast, Roland
CORPORATE BODY NAME - ALTERNATIVE RESPONSIBILITY
Institute of Physics (Great Britain),publisher.
ORIGINATING SOURCE
Date of Transaction
20200822124942.0
Cataloguing Rules (Descriptive Conventions))
pn
ELECTRONIC LOCATION AND ACCESS
Electronic name
مطالعه متن کتاب [Book]
Y
