Inverse problems :: Tikhonov theory and algorithms /
Inverse problems arise in practical applications whenever one needs to deduce unknowns from observables. This monograph is a valuable contribution to the highly topical field of computational inverse problems. Both mathematical theory and numerical algorithms for model-based inverse problems are dis...
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| Hauptverfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
[Hackensack] New Jersey :
World Scientific,
2014.
|
| Schriftenreihe: | Series on applied mathematics.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Inverse problems arise in practical applications whenever one needs to deduce unknowns from observables. This monograph is a valuable contribution to the highly topical field of computational inverse problems. Both mathematical theory and numerical algorithms for model-based inverse problems are discussed in detail. The mathematical theory focuses on nonsmooth Tikhonov regularization for linear and nonlinear inverse problems. The computational methods include nonsmooth optimization algorithms, direct inversion methods and uncertainty quantification via Bayesian inference. The book offers a com. |
| Beschreibung: | 1 online resource |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9814596205 9789814596206 |
Internformat
MARC
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| 245 | 1 | 0 | |a Inverse problems : |b Tikhonov theory and algorithms / |c by Kazufumi Ito (North Carolina State University, USA) & Bangti Jin (University of California, Riverside, USA). |
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| 490 | 1 | |a Series on Applied Mathematics ; |v v. 22 | |
| 504 | |a Includes bibliographical references and index. | ||
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| 505 | 0 | |a Preface; Contents; 1. Introduction; 2. Models in Inverse Problems; 2.1 Introduction; 2.2 Elliptic inverse problems; 2.2.1 Cauchy problem; 2.2.2 Inverse source problem; 2.2.3 Inverse scattering problem; 2.2.4 Inverse spectral problem; 2.3 Tomography; 2.3.1 Computerized tomography; 2.3.2 Emission tomography; 2.3.3 Electrical impedance tomography; 2.3.4 Optical tomography; 2.3.5 Photoacoustic tomography; 3. Tikhonov Theory for Linear Problems; 3.1 Well-posedness; 3.2 Value function calculus; 3.3 Basic estimates; 3.3.1 Classical source condition; 3.3.2 Higher-order source condition. | |
| 505 | 8 | |a 3.4 A posteriori parameter choice rules3.4.1 Discrepancy principle; 3.4.2 Hanke-Raus rule; 3.4.3 Quasi-optimality criterion; 3.5 Augmented Tikhonov regularization; 3.5.1 Augmented Tikhonov regularization; 3.5.2 Variational characterization; 3.5.3 Fixed point algorithm; 3.6 Multi-parameter Tikhonov regularization; 3.6.1 Balancing principle; 3.6.2 Error estimates; 3.6.3 Numerical algorithms; Bibliographical notes; 4. Tikhonov Theory for Nonlinear Inverse Problems; 4.1 Well-posedness; 4.2 Classical convergence rate analysis; 4.2.1 A priori parameter choice; 4.2.2 A posteriori parameter choice. | |
| 505 | 8 | |a 4.2.3 Structural properties4.3 A new convergence rate analysis; 4.3.1 Necessary optimality condition; 4.3.2 Source and nonlinearity conditions; 4.3.3 Convergence rate analysis; 4.4 A class of parameter identification problems; 4.4.1 A general class of nonlinear inverse problems; 4.4.2 Bilinear problems; 4.4.3 Three elliptic examples; 4.5 Convergence rate analysis in Banach spaces; 4.5.1 Extensions of the classical approach; 4.5.2 Variational inequalities; 4.6 Conditional stability; Bibliographical notes; 5. Nonsmooth Optimization; 5.1 Existence and necessary optimality condition. | |
| 505 | 8 | |a 5.1.1 Existence of minimizers5.1.2 Necessary optimality; 5.2 Nonsmooth optimization algorithms; 5.2.1 Augmented Lagrangian method; 5.2.2 Lagrange multiplier theory; 5.2.3 Exact penalty method; 5.2.4 Gauss-Newton method; 5.2.5 Semismooth Newton Method; 5.3 p sparsity optimization; 5.3.1 0 optimization; 5.3.2 p (0 <p <1)-optimization; 5.3.3 Primal-dual active set method; 5.4 Nonsmooth nonconvex optimization; 5.4.1 Biconjugate function and relaxation; 5.4.2 Semismooth Newton method; 5.4.3 Constrained optimization; 6. Direct Inversion Methods; 6.1 Inverse scattering methods. | |
| 505 | 8 | |a 6.1.1 The MUSIC algorithm6.1.2 Linear sampling method; 6.1.3 Direct sampling method; 6.2 Point source identification; 6.3 Numerical unique continuation; 6.4 Gel'fand-Levitan-Marchenko transformation; 6.4.1 Gel'fand-Levitan-Marchenko transformation; 6.4.2 Application to inverse Sturm-Liouville problem; Bibliographical notes; 7. Bayesian Inference; 7.1 Fundamentals of Bayesian inference; 7.2 Model selection; 7.3 Markov chain Monte Carlo; 7.3.1 Monte Carlo simulation; 7.3.2 MCMC algorithms; 7.3.3 Convergence analysis; 7.3.4 Accelerating MCMC algorithms; 7.4 Approximate inference. | |
| 520 | |a Inverse problems arise in practical applications whenever one needs to deduce unknowns from observables. This monograph is a valuable contribution to the highly topical field of computational inverse problems. Both mathematical theory and numerical algorithms for model-based inverse problems are discussed in detail. The mathematical theory focuses on nonsmooth Tikhonov regularization for linear and nonlinear inverse problems. The computational methods include nonsmooth optimization algorithms, direct inversion methods and uncertainty quantification via Bayesian inference. The book offers a com. | ||
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| 650 | 7 | |a MATHEMATICS |x Calculus. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Mathematical Analysis. |2 bisacsh | |
| 650 | 7 | |a Inverse problems (Differential equations) |x Numerical solutions |2 fast | |
| 700 | 1 | |a Jin, Bangti, |e author. | |
| 776 | 0 | 8 | |i Print version: |z 9789814596190 |z 9814596191 |w (DLC) 2014013310 |
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Datensatz im Suchindex
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| _version_ | 1816882290833227776 |
| adam_text | |
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| author | Ito, Kazufumi Jin, Bangti |
| author_facet | Ito, Kazufumi Jin, Bangti |
| author_role | aut aut |
| author_sort | Ito, Kazufumi |
| author_variant | k i ki b j bj |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA371 |
| callnumber-raw | QA371 .I88 2014 |
| callnumber-search | QA371 .I88 2014 |
| callnumber-sort | QA 3371 I88 42014 |
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| contents | Preface; Contents; 1. Introduction; 2. Models in Inverse Problems; 2.1 Introduction; 2.2 Elliptic inverse problems; 2.2.1 Cauchy problem; 2.2.2 Inverse source problem; 2.2.3 Inverse scattering problem; 2.2.4 Inverse spectral problem; 2.3 Tomography; 2.3.1 Computerized tomography; 2.3.2 Emission tomography; 2.3.3 Electrical impedance tomography; 2.3.4 Optical tomography; 2.3.5 Photoacoustic tomography; 3. Tikhonov Theory for Linear Problems; 3.1 Well-posedness; 3.2 Value function calculus; 3.3 Basic estimates; 3.3.1 Classical source condition; 3.3.2 Higher-order source condition. 3.4 A posteriori parameter choice rules3.4.1 Discrepancy principle; 3.4.2 Hanke-Raus rule; 3.4.3 Quasi-optimality criterion; 3.5 Augmented Tikhonov regularization; 3.5.1 Augmented Tikhonov regularization; 3.5.2 Variational characterization; 3.5.3 Fixed point algorithm; 3.6 Multi-parameter Tikhonov regularization; 3.6.1 Balancing principle; 3.6.2 Error estimates; 3.6.3 Numerical algorithms; Bibliographical notes; 4. Tikhonov Theory for Nonlinear Inverse Problems; 4.1 Well-posedness; 4.2 Classical convergence rate analysis; 4.2.1 A priori parameter choice; 4.2.2 A posteriori parameter choice. 4.2.3 Structural properties4.3 A new convergence rate analysis; 4.3.1 Necessary optimality condition; 4.3.2 Source and nonlinearity conditions; 4.3.3 Convergence rate analysis; 4.4 A class of parameter identification problems; 4.4.1 A general class of nonlinear inverse problems; 4.4.2 Bilinear problems; 4.4.3 Three elliptic examples; 4.5 Convergence rate analysis in Banach spaces; 4.5.1 Extensions of the classical approach; 4.5.2 Variational inequalities; 4.6 Conditional stability; Bibliographical notes; 5. Nonsmooth Optimization; 5.1 Existence and necessary optimality condition. 5.1.1 Existence of minimizers5.1.2 Necessary optimality; 5.2 Nonsmooth optimization algorithms; 5.2.1 Augmented Lagrangian method; 5.2.2 Lagrange multiplier theory; 5.2.3 Exact penalty method; 5.2.4 Gauss-Newton method; 5.2.5 Semismooth Newton Method; 5.3 p sparsity optimization; 5.3.1 0 optimization; 5.3.2 p (0 <p <1)-optimization; 5.3.3 Primal-dual active set method; 5.4 Nonsmooth nonconvex optimization; 5.4.1 Biconjugate function and relaxation; 5.4.2 Semismooth Newton method; 5.4.3 Constrained optimization; 6. Direct Inversion Methods; 6.1 Inverse scattering methods. 6.1.1 The MUSIC algorithm6.1.2 Linear sampling method; 6.1.3 Direct sampling method; 6.2 Point source identification; 6.3 Numerical unique continuation; 6.4 Gel'fand-Levitan-Marchenko transformation; 6.4.1 Gel'fand-Levitan-Marchenko transformation; 6.4.2 Application to inverse Sturm-Liouville problem; Bibliographical notes; 7. Bayesian Inference; 7.1 Fundamentals of Bayesian inference; 7.2 Model selection; 7.3 Markov chain Monte Carlo; 7.3.1 Monte Carlo simulation; 7.3.2 MCMC algorithms; 7.3.3 Convergence analysis; 7.3.4 Accelerating MCMC algorithms; 7.4 Approximate inference. |
| ctrlnum | (OCoLC)893487334 |
| dewey-full | 515/.357 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.357 |
| dewey-search | 515/.357 |
| dewey-sort | 3515 3357 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn893487334 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:26:16Z |
| institution | BVB |
| isbn | 9814596205 9789814596206 |
| language | English |
| oclc_num | 893487334 |
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| publisher | World Scientific, |
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| series | Series on applied mathematics. |
| series2 | Series on Applied Mathematics ; |
| spelling | Ito, Kazufumi, author. Inverse problems : Tikhonov theory and algorithms / by Kazufumi Ito (North Carolina State University, USA) & Bangti Jin (University of California, Riverside, USA). [Hackensack] New Jersey : World Scientific, 2014. 1 online resource text txt rdacontent computer c rdamedia online resource cr rdacarrier Series on Applied Mathematics ; v. 22 Includes bibliographical references and index. Print version record. Preface; Contents; 1. Introduction; 2. Models in Inverse Problems; 2.1 Introduction; 2.2 Elliptic inverse problems; 2.2.1 Cauchy problem; 2.2.2 Inverse source problem; 2.2.3 Inverse scattering problem; 2.2.4 Inverse spectral problem; 2.3 Tomography; 2.3.1 Computerized tomography; 2.3.2 Emission tomography; 2.3.3 Electrical impedance tomography; 2.3.4 Optical tomography; 2.3.5 Photoacoustic tomography; 3. Tikhonov Theory for Linear Problems; 3.1 Well-posedness; 3.2 Value function calculus; 3.3 Basic estimates; 3.3.1 Classical source condition; 3.3.2 Higher-order source condition. 3.4 A posteriori parameter choice rules3.4.1 Discrepancy principle; 3.4.2 Hanke-Raus rule; 3.4.3 Quasi-optimality criterion; 3.5 Augmented Tikhonov regularization; 3.5.1 Augmented Tikhonov regularization; 3.5.2 Variational characterization; 3.5.3 Fixed point algorithm; 3.6 Multi-parameter Tikhonov regularization; 3.6.1 Balancing principle; 3.6.2 Error estimates; 3.6.3 Numerical algorithms; Bibliographical notes; 4. Tikhonov Theory for Nonlinear Inverse Problems; 4.1 Well-posedness; 4.2 Classical convergence rate analysis; 4.2.1 A priori parameter choice; 4.2.2 A posteriori parameter choice. 4.2.3 Structural properties4.3 A new convergence rate analysis; 4.3.1 Necessary optimality condition; 4.3.2 Source and nonlinearity conditions; 4.3.3 Convergence rate analysis; 4.4 A class of parameter identification problems; 4.4.1 A general class of nonlinear inverse problems; 4.4.2 Bilinear problems; 4.4.3 Three elliptic examples; 4.5 Convergence rate analysis in Banach spaces; 4.5.1 Extensions of the classical approach; 4.5.2 Variational inequalities; 4.6 Conditional stability; Bibliographical notes; 5. Nonsmooth Optimization; 5.1 Existence and necessary optimality condition. 5.1.1 Existence of minimizers5.1.2 Necessary optimality; 5.2 Nonsmooth optimization algorithms; 5.2.1 Augmented Lagrangian method; 5.2.2 Lagrange multiplier theory; 5.2.3 Exact penalty method; 5.2.4 Gauss-Newton method; 5.2.5 Semismooth Newton Method; 5.3 p sparsity optimization; 5.3.1 0 optimization; 5.3.2 p (0 <p <1)-optimization; 5.3.3 Primal-dual active set method; 5.4 Nonsmooth nonconvex optimization; 5.4.1 Biconjugate function and relaxation; 5.4.2 Semismooth Newton method; 5.4.3 Constrained optimization; 6. Direct Inversion Methods; 6.1 Inverse scattering methods. 6.1.1 The MUSIC algorithm6.1.2 Linear sampling method; 6.1.3 Direct sampling method; 6.2 Point source identification; 6.3 Numerical unique continuation; 6.4 Gel'fand-Levitan-Marchenko transformation; 6.4.1 Gel'fand-Levitan-Marchenko transformation; 6.4.2 Application to inverse Sturm-Liouville problem; Bibliographical notes; 7. Bayesian Inference; 7.1 Fundamentals of Bayesian inference; 7.2 Model selection; 7.3 Markov chain Monte Carlo; 7.3.1 Monte Carlo simulation; 7.3.2 MCMC algorithms; 7.3.3 Convergence analysis; 7.3.4 Accelerating MCMC algorithms; 7.4 Approximate inference. Inverse problems arise in practical applications whenever one needs to deduce unknowns from observables. This monograph is a valuable contribution to the highly topical field of computational inverse problems. Both mathematical theory and numerical algorithms for model-based inverse problems are discussed in detail. The mathematical theory focuses on nonsmooth Tikhonov regularization for linear and nonlinear inverse problems. The computational methods include nonsmooth optimization algorithms, direct inversion methods and uncertainty quantification via Bayesian inference. The book offers a com. Inverse problems (Differential equations) Numerical solutions. http://id.loc.gov/authorities/subjects/sh85067685 Problèmes inverses (Équations différentielles) Solutions numériques. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Inverse problems (Differential equations) Numerical solutions fast Jin, Bangti, author. Print version: 9789814596190 9814596191 (DLC) 2014013310 Series on applied mathematics. http://id.loc.gov/authorities/names/n93008796 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=862357 Volltext |
| spellingShingle | Ito, Kazufumi Jin, Bangti Inverse problems : Tikhonov theory and algorithms / Series on applied mathematics. Preface; Contents; 1. Introduction; 2. Models in Inverse Problems; 2.1 Introduction; 2.2 Elliptic inverse problems; 2.2.1 Cauchy problem; 2.2.2 Inverse source problem; 2.2.3 Inverse scattering problem; 2.2.4 Inverse spectral problem; 2.3 Tomography; 2.3.1 Computerized tomography; 2.3.2 Emission tomography; 2.3.3 Electrical impedance tomography; 2.3.4 Optical tomography; 2.3.5 Photoacoustic tomography; 3. Tikhonov Theory for Linear Problems; 3.1 Well-posedness; 3.2 Value function calculus; 3.3 Basic estimates; 3.3.1 Classical source condition; 3.3.2 Higher-order source condition. 3.4 A posteriori parameter choice rules3.4.1 Discrepancy principle; 3.4.2 Hanke-Raus rule; 3.4.3 Quasi-optimality criterion; 3.5 Augmented Tikhonov regularization; 3.5.1 Augmented Tikhonov regularization; 3.5.2 Variational characterization; 3.5.3 Fixed point algorithm; 3.6 Multi-parameter Tikhonov regularization; 3.6.1 Balancing principle; 3.6.2 Error estimates; 3.6.3 Numerical algorithms; Bibliographical notes; 4. Tikhonov Theory for Nonlinear Inverse Problems; 4.1 Well-posedness; 4.2 Classical convergence rate analysis; 4.2.1 A priori parameter choice; 4.2.2 A posteriori parameter choice. 4.2.3 Structural properties4.3 A new convergence rate analysis; 4.3.1 Necessary optimality condition; 4.3.2 Source and nonlinearity conditions; 4.3.3 Convergence rate analysis; 4.4 A class of parameter identification problems; 4.4.1 A general class of nonlinear inverse problems; 4.4.2 Bilinear problems; 4.4.3 Three elliptic examples; 4.5 Convergence rate analysis in Banach spaces; 4.5.1 Extensions of the classical approach; 4.5.2 Variational inequalities; 4.6 Conditional stability; Bibliographical notes; 5. Nonsmooth Optimization; 5.1 Existence and necessary optimality condition. 5.1.1 Existence of minimizers5.1.2 Necessary optimality; 5.2 Nonsmooth optimization algorithms; 5.2.1 Augmented Lagrangian method; 5.2.2 Lagrange multiplier theory; 5.2.3 Exact penalty method; 5.2.4 Gauss-Newton method; 5.2.5 Semismooth Newton Method; 5.3 p sparsity optimization; 5.3.1 0 optimization; 5.3.2 p (0 <p <1)-optimization; 5.3.3 Primal-dual active set method; 5.4 Nonsmooth nonconvex optimization; 5.4.1 Biconjugate function and relaxation; 5.4.2 Semismooth Newton method; 5.4.3 Constrained optimization; 6. Direct Inversion Methods; 6.1 Inverse scattering methods. 6.1.1 The MUSIC algorithm6.1.2 Linear sampling method; 6.1.3 Direct sampling method; 6.2 Point source identification; 6.3 Numerical unique continuation; 6.4 Gel'fand-Levitan-Marchenko transformation; 6.4.1 Gel'fand-Levitan-Marchenko transformation; 6.4.2 Application to inverse Sturm-Liouville problem; Bibliographical notes; 7. Bayesian Inference; 7.1 Fundamentals of Bayesian inference; 7.2 Model selection; 7.3 Markov chain Monte Carlo; 7.3.1 Monte Carlo simulation; 7.3.2 MCMC algorithms; 7.3.3 Convergence analysis; 7.3.4 Accelerating MCMC algorithms; 7.4 Approximate inference. Inverse problems (Differential equations) Numerical solutions. http://id.loc.gov/authorities/subjects/sh85067685 Problèmes inverses (Équations différentielles) Solutions numériques. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Inverse problems (Differential equations) Numerical solutions fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85067685 |
| title | Inverse problems : Tikhonov theory and algorithms / |
| title_auth | Inverse problems : Tikhonov theory and algorithms / |
| title_exact_search | Inverse problems : Tikhonov theory and algorithms / |
| title_full | Inverse problems : Tikhonov theory and algorithms / by Kazufumi Ito (North Carolina State University, USA) & Bangti Jin (University of California, Riverside, USA). |
| title_fullStr | Inverse problems : Tikhonov theory and algorithms / by Kazufumi Ito (North Carolina State University, USA) & Bangti Jin (University of California, Riverside, USA). |
| title_full_unstemmed | Inverse problems : Tikhonov theory and algorithms / by Kazufumi Ito (North Carolina State University, USA) & Bangti Jin (University of California, Riverside, USA). |
| title_short | Inverse problems : |
| title_sort | inverse problems tikhonov theory and algorithms |
| title_sub | Tikhonov theory and algorithms / |
| topic | Inverse problems (Differential equations) Numerical solutions. http://id.loc.gov/authorities/subjects/sh85067685 Problèmes inverses (Équations différentielles) Solutions numériques. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Inverse problems (Differential equations) Numerical solutions fast |
| topic_facet | Inverse problems (Differential equations) Numerical solutions. Problèmes inverses (Équations différentielles) Solutions numériques. MATHEMATICS Calculus. MATHEMATICS Mathematical Analysis. Inverse problems (Differential equations) Numerical solutions |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=862357 |
| work_keys_str_mv | AT itokazufumi inverseproblemstikhonovtheoryandalgorithms AT jinbangti inverseproblemstikhonovtheoryandalgorithms |