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008			091123s2015 si a sb 001 0 eng d
010			_a2014013310
020			_a9789814596213
040			_aWSPC _beng _cWSPC
050	0	4	_aQA371 _b.I88 2014
082	0	4	_a515.357
100	1		_aIto, Kazufumi and Jin, Bangti
245	1	0	_aInverse Problems : _bTikhonov Theory and Algorithms /
260			_aSingapore ; _bWorld Scientific Pub. Co., _cc2015.
300			_a332 p. :
440			_aSeries on Applied Mathematics: _vVol. 22 ;
505	0		_a1. Introduction -- 2. Models in inverse problems. 2.1. Introduction. 2.2. Elliptic inverse problems. 2.3. Tomography -- 3. Tikhonov theory for linear problems. 3.1. Well-posedness. 3.2. Value function calculus. 3.3. Basic estimates. 3.4. A posteriori parameter choice rules. 3.5. Augmented Tikhonov regularization. 3.6. Multi-parameter Tikhonov regularization -- 4. Tikhonov theory for nonlinear inverse problems. 4.1. Well-posedness. 4.2. Classical convergence rate analysis. 4.3. A new convergence rate analysis. 4.4. A class of parameter identification problems. 4.5. Convergence rate analysis in Banach spaces. 4.6. Conditional stability -- 5. Nonsmooth optimization. 5.1. Existence and necessary optimality condition. 5.2. Nonsmooth optimization algorithms. 5.3. [symbol] sparsity optimization. 5.4. Nonsmooth nonconvex optimization -- 6. Direct inversion methods. 6.1. Inverse scattering methods. 6.2. Point source identification. 6.3. Numerical unique continuation. 6.4. Gel'fand-Levitan-Marchenko transformation -- 7. Bayesian inference. 7.1. Fundamentals of Bayesian inference. 7.2. Model selection. 7.3. Markov chain Monte Carlo. 7.4. Approximate inference.
520			_aInverse 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 comprehensive treatment of modern techniques, and seamlessly blends regularization theory with computational methods, which is essential for developing accurate and efficient inversion algorithms for many practical inverse problems. It demonstrates many current developments in the field of computational inversion, such as value function calculus, augmented Tikhonov regularization, multi-parameter Tikhonov regularization, semismooth Newton method, direct sampling method, uncertainty quantification and approximate Bayesian inference. It is written for graduate students and researchers in mathematics, natural science and engineering.
533			_aElectronic reproduction. _bSingapore : _cWorld Scientific Publishing Co., _d2015. _nSystem requirements: Adobe Acrobat Reader. _nMode of access: World Wide Web. _nAvailable to subscribing institutions.
650		0	_aInverse problems (Differential equations) _xNumerical solutions.
655		0	_aElectronic books.
776	1		_z9789814596190
856	4	0	_uhttp://www.worldscientific.com/worldscibooks/10.1142/9120#t=toc
942			_2ddc _cEBK
999			_c2365 _d2365