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Numerical Methods for Inverse Problems. (Record no. 109231)

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000 -LEADER
fixed length control field 05984nam a22004573i 4500
001 - CONTROL NUMBER
control field EBC4501313
003 - CONTROL NUMBER IDENTIFIER
control field MiAaPQ
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20240729130430.0
006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS
fixed length control field m o d |
007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION
fixed length control field cr cnu||||||||
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 240724s2016 xx o ||||0 eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9781119136958
Qualifying information (electronic bk.)
035 ## - SYSTEM CONTROL NUMBER
System control number (MiAaPQ)EBC4501313
035 ## - SYSTEM CONTROL NUMBER
System control number (Au-PeEL)EBL4501313
035 ## - SYSTEM CONTROL NUMBER
System control number (CaPaEBR)ebr11202282
035 ## - SYSTEM CONTROL NUMBER
System control number (CaONFJC)MIL910405
035 ## - SYSTEM CONTROL NUMBER
System control number (OCoLC)945976688
040 ## - CATALOGING SOURCE
Original cataloging agency MiAaPQ
Language of cataloging eng
Description conventions rda
-- pn
Transcribing agency MiAaPQ
Modifying agency MiAaPQ
050 #4 - LIBRARY OF CONGRESS CALL NUMBER
Classification number QA378.5.K47 2016
082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 515/.357
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Kern, Michel.
245 10 - TITLE STATEMENT
Title Numerical Methods for Inverse Problems.
250 ## - EDITION STATEMENT
Edition statement 1st ed.
264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE
Place of production, publication, distribution, manufacture Newark :
Name of producer, publisher, distributor, manufacturer John Wiley & Sons, Incorporated,
Date of production, publication, distribution, manufacture, or copyright notice 2016.
264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE
Date of production, publication, distribution, manufacture, or copyright notice ©2016.
300 ## - PHYSICAL DESCRIPTION
Extent 1 online resource (234 pages)
336 ## - CONTENT TYPE
Content type term text
Content type code txt
Source rdacontent
337 ## - MEDIA TYPE
Media type term computer
Media type code c
Source rdamedia
338 ## - CARRIER TYPE
Carrier type term online resource
Carrier type code cr
Source rdacarrier
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note Cover -- Dedication -- Title Page -- Copyright -- Contents -- Preface -- Book layout -- Acknowledgments -- PART 1: Introduction and Examples -- 1: Overview of Inverse Problems -- 1.1. Direct and inverse problems -- 1.2. Well-posed and ill-posed problems -- 2: Examples of Inverse Problems -- 2.1. Inverse problems in heat transfer -- 2.2. Inverse problems in hydrogeology -- 2.3. Inverse problems in seismic exploration -- 2.4. Medical imaging -- 2.5. Other examples -- PART 2: Linear Inverse Problems -- 3: Integral Operators and Integral Equations -- 3.1. Definition and first properties -- 3.2. Discretization of integral equations -- 3.2.1. Discretization by quadrature-collocation -- 3.2.2. Discretization by the Galerkin method -- 3.3. Exercises -- 4: Linear Least Squares Problems - Singular Value Decomposition -- 4.1. Mathematical properties of least squares problems -- 4.1.1. Finite dimensional case -- 4.2. Singular value decomposition for matrices -- 4.3. Singular value expansion for compact operators -- 4.4. Applications of the SVD to least squares problems -- 4.4.1. The matrix case -- 4.4.2. The operator case -- 4.5. Exercises -- 5: Regularization of Linear Inverse Problems -- 5.1. Tikhonov's method -- 5.1.1. Presentation -- 5.1.2. Convergence -- 5.1.3. The L-curve -- 5.2. Applications of the SVE -- 5.2.1. Singular value expansion and Tikhonov's method -- 5.2.2. Regularization by truncated SVE -- 5.3. Choice of the regularization parameter -- 5.3.1. Morozov's discrepancy principle -- 5.3.2. The L-curve -- 5.3.3. Numerical methods -- 5.4. Iterative methods -- 5.5. Exercises -- PART 3: Nonlinear Inverse Problems -- 6: Nonlinear Inverse Problems - Generalities -- 6.1. The three fundamental spaces -- 6.2. Least squares formulation -- 6.2.1. Difficulties of inverse problems -- 6.2.2. Optimization, parametrization, discretization.
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note 6.3. Methods for computing the gradient - the adjoint state method -- 6.3.1. The finite difference method -- 6.3.2. Sensitivity functions -- 6.3.3. The adjoint state method -- 6.3.4. Computation of the adjoint state by the Lagrangian -- 6.3.5. The inner product test -- 6.4. Parametrization and general organization -- 6.5. Exercises -- 7: Some Parameter Estimation Examples -- 7.1. Elliptic equation in one dimension -- 7.1.1. Computation of the gradient -- 7.2. Stationary diffusion: elliptic equation in two dimensions -- 7.2.1. Computation of the gradient: application of the general method -- 7.2.2. Computation of the gradient by the Lagrangian -- 7.2.3. The inner product test -- 7.2.4. Multiscale parametrization -- 7.2.5. Example -- 7.3. Ordinary differential equations -- 7.3.1. An application example -- 7.4. Transient diffusion: heat equation -- 7.5. Exercises -- 8: Further Information -- 8.1. Regularization in other norms -- 8.1.1. Sobolev semi-norms -- 8.1.2. Bounded variation regularization norm -- 8.2. Statistical approach: Bayesian inversion -- 8.2.1. Least squares and statistics -- 8.2.2. Bayesian inversion -- 8.2.2.1. A priori and a posteriori probabilities -- 8.2.2.2. A few estimation techniques -- 8.2.2.3. References -- 8.3. Other topics -- 8.3.1. Theoretical aspects: identifiability -- 8.3.2. Algorithmic differentiation -- 8.3.3. Iterative methods and large-scale problems -- 8.3.4. Software -- Appendices -- Appendix 1: Numerical Methods for Least Squares Problems -- A1.1. Conditioning of the least squares problems -- A1.2. Normal equations -- A1.3. QR factorization -- A1.3.1. Householder matrices -- A1.3.2. QR factorization -- A1.3.3. Solution of the least squares problem -- A1.4. SVD and numerical methods -- Appendix 2: Optimization Refreshers -- A2.1. Local and global algorithms -- A2.2. Gradients, Hessians and optimality conditions.
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note A2.3. Quasi-Newton methods -- A2.4. Nonlinear least squares and the Gauss-Newton method -- Appendix 3: Some Results from Functional Analysis -- A3.1. Hilbert spaces -- A3.1.1. Definitions and examples -- A3.1.2. Properties of Hilbert spaces -- A3.1.3. Hilbert bases -- A3.2. Linear operators in Hilbert spaces -- A3.2.1. General properties -- A3.2.2. Adjoint operator -- A3.2.3. Compact operators -- A3.3. Spectral decomposition of compact self-adjoint operators -- Bibliography -- Index -- EULA.
588 ## - SOURCE OF DESCRIPTION NOTE
Source of description note Description based on publisher supplied metadata and other sources.
590 ## - LOCAL NOTE (RLIN)
Local note Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Inverse problems (Differential equations)--Numerical solutions.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Inverse problems (Differential equations)--Numerical solutions. (OCoLC)fst00978099.
655 #4 - INDEX TERM--GENRE/FORM
Genre/form data or focus term Electronic books.
776 08 - ADDITIONAL PHYSICAL FORM ENTRY
Relationship information Print version:
Main entry heading Kern, Michel
Title Numerical Methods for Inverse Problems
Place, publisher, and date of publication Newark : John Wiley & Sons, Incorporated,c2016
797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN)
Corporate name or jurisdiction name as entry element ProQuest (Firm)
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4501313">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4501313</a>
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