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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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
[Hackensack] New Jersey :
World Scientific,
2014.
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| Colección: | Series on applied mathematics.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Ito, Kazufumi, |e author. | |
| 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). |
| 264 | 1 | |a [Hackensack] New Jersey : |b World Scientific, |c 2014. | |
| 300 | |a 1 online resource | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 490 | 1 | |a Series on Applied Mathematics ; |v v. 22 | |
| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Print version record. | |
| 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. | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Inverse problems (Differential equations) |x Numerical solutions. | |
| 650 | 6 | |a Problèmes inverses (Équations différentielles) |x Solutions numériques. | |
| 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 |
| 830 | 0 | |a Series on applied mathematics. | |
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