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| Авторизация |
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| Поиск по указателям |
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| Vogel C.R. — Computational Methods for Inverse Problems (Frontiers in Applied Mathematics) |
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| Предметный указатель |
 method 98
Active set 155
Asymptotic equality 114
Autocorrelation 50
Bayes’ Law 48
Best linear unbiased estimator 51
BFGS method 36
BFGS method, limited memory 36
Big “O” notation 114
Binding set 162
Bounded variation 147
Circulant, block matrix 72
Circulant, matrix 68
Circulant, right shift matrix 69
Compact operator 17
Complementarity 155
Complementarity for nonnegativity 156
Complementarity, strict 155
Condition number 30
Conditional, expectation 47
Conditional, probability 47
Conjugate gradient method, linear 31
Conjugate gradient method, nonlinear 34
Conjugate gradient method, preconditioned 33
Conjugate, functional 136
Conjugate, set 136
Convergence rate, linear 29
Convergence rate, quadratic 29
Convergence rate, superlinear 29
Convex, functional 21
Convex, projection 155
Convex, set 21
Convolution theorem 60
Convolution, continuous one-dimensional 1
Convolution, continuous two-dimensional 59
Convolution, discrete one-dimensional 64
Convolution, discrete two-dimensional 65
Covariance 45
Cross correlation 50
Cumulative distribution function 42
Deblurring 59
Degenerate critical point 156
Descent direction 30
Dirichlet boundary conditions 75
Discrepancy principle 8 104
Distributed parameter system 86
Divergence 145
Dual representation 137
EMLS algorithm 166
Energy, inner product 30
Energy, norm 30
entropy 25
Estimation error 97
Expectation maximization algorithm 54 165
Expected value 45
Face 160
Fast Fourier Transform 66
Fast Fourier transform, two-dimensional 67
Feasible, point 154
Feasible, set 154
Fenchel transform 136
Filter function 3
Finite element method 90
Fourier, continuous transform 60 181 182
Fourier, discrete one-dimensional transform 64
Fourier, discrete two-dimensional transform 65
Fourier, matrix 64
Frechet derivative 22
Fredholm first kind integral equation 1
Free variables 155
Frobenius 14
Galerkin’s method 90
Gateaux derivative 22
Gauss — Markov theorem 51
Gauss — Newton approximation 89
Gaussian distribution 45
Generalized cross validation 103
Generalized inverse 18
Globalization 35
Gradient 22
Gradient projection conjugate gradient method 161
Gradient projection method 157
Gram matrix 16
harmonic oscillator 85
hessian 24
Huber function 132
Ill-posed equation 16
Inactive set 155
Independence 44
Influence matrix 98 110
Karush — Kuhn — Tucker conditions 155
| Kullback-Leibler information divergence 25
L-curve 106
Lagged diffusivity fixed point iteration 135
Lagrange multiplier 155
Landweber iteration 10
Laplacian, discrete 74
Least squares solution 19
Levenberg — Marquardt method 89
lexicographical ordering 71
Likelihood function 46
Line search 30
Line search, inexact 36
Line search, projected 158
Line search, quadratic backtracking 38
Linear independence constraint qualification 155
Load vector 91
Log likelihood function 46
Maximum a posteriori estimator 48
Maximum likelihood estimator 46
Mean 45
Mean squared predictive error 98
Minimum bound method 107
Modified residual norm steepest descent algorithm 169
Neumann boundary conditions 75
Newton’s method 34
Nondegenerate critical point 156
Nonnegativity constraints 151
Normal equations 76
Order optimal 8
Orthonormal 16
Output least squares 86 87
Parameter identification 85
Penalty functional 24
Periodic extension in one dimension 64
Periodic extension in two dimensions 65
Point spread function 59
Poisson distribution 45
Positive, definite 14
Positive, semidefinite 14
Predictive error 97 110
Predictive risk 98
Primal-dual Newton method 136
Prior 49
Probability, density function 42
Probability, joint 46
Probability, marginal 46
Probability, mass function 42
Probability, space 41
Projected gradient 156
Projected Newton method 158
Pseudo-inverse 18
Random variable 42
Randomized trace estimate 101
Rank 18
Reduced Hessian 159
Regular point 155
Regularization, functional 24
Regularization, generalized Tikhonov 24
Regularization, parameter 5
Regularized residual 99
Richardson — Lucy iteration 165
Sample space 41
Saturation 119
Self-adjoint operator 14
Singular system 17
Singular value decomposition 3 18
Source condition 7
State, equation 86
State, variable 85
Steepest descent method 30
Stiffness matrix 91
Strong positivity 14
Symmetric, positive definite 29
System parameters 85
Tensor product 72
Tikhonov 5
Toeplitz, block matrix 71
Toeplitz, matrix 68
Total variation 9 129
Trace 50
Trace Lemma 98
Truncated singular value decomposition 5
Trust region 35
Unbiased predictive risk estimator 99
Unbiased predictive risk estimator method 98
Uniform distribution 43
Weak, convergence 21
Weak, lower semicontinuity 21
Well-posed equation 16
White noise 98
Wolfe conditions 37
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