反问题的计算方法
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作者（美）沃格尔 著
出版社清华大学出版社
ISBN9787302245025
出版时间2011-02
版次1
装帧平装
开本16开
纸张胶版纸
页数183页
定价28元
上书时间2024-07-01
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基本信息
书名:反问题的计算方法
定价：28元
作者:（美）沃格尔 著
出版社：清华大学出版社
出版日期：2011-02-01
ISBN：9787302245025
字数：
页码：183
版次：1
装帧：平装
开本：16开
商品重量：
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目录
《反问题的计算方法(英文)》forewordpreface1 introductio 1.1 an illustrative example 1.2 regularization by filtering 1.2.1 a deterministic error analysis 1.2.2 rates of convergence 1.2.3 a posteriori regularization parameter selectio 1.3 variational regularization methods 1.4 iterative regularization methods exercises2 analytical tools 2.1 ill-posedness and regularizatio 2.1.1 compact operators, singular systems, and the svd 2.1.2 least squares solutions and the pseudo-inverse 2.2 regularization theory 2.3 optimization theory 2.4 generalized tikhonov regularizatio 2.4.1 penalty functionals 2.4.2 data discrepancy functionals 2.4.3 some analysis exercises3 numerical optimization tools 3.1 the steepest descent method 3.2 the conjugate gradient method 3.2.1 preconditioning 3.2.2 nonlinear cg method 3.3 newton's method 3.3.1 trust region globalization of newton's method 3.3.2 the bfgs method 3.4 inexact line search exercises4 statistical estimation theory 4.1 preliminary definitions and notatio 4.2 mamum likelihood'estimatio 4.3 bayesian estimatio 4.4 linear least squares estimatio 4.4.1 best linear unbiased estimatio 4.4.2 minimum variance linear estimatio 4.5 the em algorithm 4.5.1 an illustrative example exercises5 image deblurring 5.1 a mathematical model for image blurring 5.1.1 a two-dimensional test problem 5.2 computational methods for toeplitz systems 5.2.1 discrete fourier transform and convolutio 5.2.2 the fft a, lgorithm 5.2.3 toeplitz and circulant matrices 5.2.4 best circulant appromatio 5.2.5 block toeplitz and block circulant matrices 5.3 fourier-based deblurring methods 5.3.1 direct fourier inversio 5.3.2 cg for block toeplitz systems 5.3.3 block circulant preconditioners 5.3.4 a comparison of block circulant preconditioners 5.4 multilevel techniques exercises6 parameter identificatio 6.1 an abstract framework 6.1.1 gradient computations 6.1.2 adjoint, or costate, methods 6.1.3 hessian computations 6.1.4 gauss-newton hessian appromatio 6.2 a one-dimensional example 6.3 a convergence result exercises7 regularization parameter selection methods 7.1 the unbiased predictive risk estimator method 7.1.1 implementation of the upre method 7.1.2 randomized trace estimatio 7.1.3 a numerical illustration of trace estimatio 7.1.4 nonlinear variants of upre 7.2 generalized cross validatio 7.2.1 a numerical comparison of upre and gcv 7.3 the discrepancy principle 7.3. i implementation of the discrepancy principle 7.4 the l-curve method 7.4.1 a numerical illustration of the l-curve method 7.5 other regularization parameter selection methods 7.6 analysis of regularization parameter selection methods 7.6.1 model assumptions and preliminary results 7.6.2 estimation and predictive errors for tsvd 7.6.3 estimation and predictive errors for tikhonovregularizatio 7.6.4 analysis of the discrepancy principle 7.6.5 analysis of gcv 7.6.6 analysis of the l-curve method 7.7 a comparison of methods exercises8 total variation regularizatio9 nonnegativity constraintsexercisesbibliography
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