Title Inverse problems : Tikhonov theory and algorithms / by Kazufumi Ito (North Carolina State University, USA) & Bangti Jin (University of California, Riverside, USA).

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[Hackensack] New Jersey : World Scientific, 2014.

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Description	1 online resource.
	text file
Series	Series on Applied Mathematics ; v.22
	Series on applied mathematics.
Bibliography	Includes bibliographical references and index.
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.
Summary	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.
Local Note	eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America
Subject	Inverse problems (Differential equations) -- Numerical solutions.
	Inverse problems (Differential equations) -- Numerical solutions.
Genre/Form	Electronic books.
	Electronic books.
Added Author	Jin, Bangti, author.
Other Form:	Print version: 9789814596190 9814596191 (DLC) 2014013310
ISBN	9814596205 electronic book
	9789814596206 electronic book
	9789814596190 (hardcover) (alkaline paper)
	9814596191 (hardcover) (alkaline paper)

Title Inverse problems : Tikhonov theory and algorithms / by Kazufumi Ito (North Carolina State University, USA) & Bangti Jin (University of California, Riverside, USA).

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