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| Tarantola A. — Inverse problem theory and methods for model parameter estimation |
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| Предметный указатель |
Instrument, with additive noise 26
Instrument, with known statistics 25
Integral operator 184
Intersection 6
Intersection, of fuzzy sets 14
Invariance homogeneous probability density 11
Inverse 230
Inverse, modeling 2
Inverse, of a partitioned matrix 250
Inverse, of the covariance 188
Inverse, problem (solution) 32 33
Inversion sampling method 48
Inversion, of acoustic waveforms 297
Inversion, of elastic waveforms 144
Isometric isomorphism 241
Isomorphic, linear spaces 238
Isomorphic, spaces 231
Isomorphism 231 238
Isomorphism, isometric 241
Jacobian rule 8
Jaynes 6 11 163
Jeffreys 6 12 101 162
Jeffreys, parameter 12 162
Jeffreys, parameter (power) 163
Jeffreys, tensor 165
Jeroslow 225
Joint probability density 19
Journel 14 30
K6nig 225
Kalman filter 67 198
Kalos 42
Karal 300
Karmarkar 225
Keilis — Borok 42
Kernel 238
Kernel, operator 184
Kernel, subspace 184
Kirkpatrick 54
Klee 225
Kolmogorov axioms 6
Koren 47
Kupferschmid 225
Lagrange parameters 73 249
Landa 38
Landau 145
Lang 2
Laplace xii 64 81
Laplace distribution 89
Laplace function 81
Large residuals 74
Laws physical 2
Lay 109
Least squares 57 62
Least squares, function 64
Least squares, norm 236
Least-absolute-values criterion 81 89
Lee 72
legendre xii
Levenberg 80
Levenberg — Marquardt 80
Lifshitz 145
Likelihood 12
Likelihood, function 34 35 39
Linear 231
Linear, form 58 239
Linear, operator 237
Linear, operator (continuous) 241
Linear, problem 64
Linear, programming 95 223
Linear, programming (dual problems) 225
Linear, programming (ti-aorm) 228
Linear, regression (uncertainties in both axes) 273
Linear, regression (usual least-squares) 269
Linear, regression (with an outlier) 275 295
Linear, regression (with rounding errors) 266
Linear, space 58 234
Linear, space (normed) 183
Linear, subspace 236
Linearly independent 236
Lions 190
Local optimum 69
Log-normal probability density 175
Long-tailed distribution 81
Lovasc 225
Luenberger 95
Magnanti 95 225
Mangasarian 225
Manifold 2 232
Mapping 230
Marginal probability density 18
Marginalizing in linear least squares 200
Markov chain Monte Carlo 50
Marquardt 80
Mass of Earth's core 9
Math optimizer (software) 80
Mathematica 80
Mathematical expectation 171 172
MATLAB 80
Matrix identities 249
Maximum entropy probability density 245
Maximum likelihood point 39
McCall 225
MCMC 50
Mean 171 172
Mean, deviation 89 171 174
Mean, sample 162
Mean, value (of a random function) 105
Measure 6
Measure, density 7
Measurement uncertainties 21
Measurements 24
Measuring travel times 25
Median 171
Metric, on a manifold 160
Metric, open subset 234
Metric, space 183 232
Metropolis 50
Metropolis — Hastings algorithm 50
Metropolis, algorithm 41 50
Metropolis, algorithm (cascaded) 51
Midrange 171 175
Mille-feuille 58 206
Minimax, criterion 98
Minimax, norm 98
Minty 225
Misfit function, for nonlinear least-squares 68
Misfit function, in  -norm problems 88
Misfit function, in least-squares 64
Model 3
Model parameters a priori information 27
Model space, finite-dimensional 3
Model space, linear 4
Model space, manifold 2
Model space, random exploration 38
Model, parameters 1
Modelization, imperfections 21
Modelization, uncertainties (negligible) 34
Models, multiplication 4
Models, sum 4
Monte Carlo method of numerical integration 179
Monte Carlo methods 41
Morgan 37
Moritz 101
Morse 145 190
Mosegaard 19 22 35 50 51 53
Movie strategy 44
Muir 81 82 96
Murray 203
Murty 95
Narasimhan 2
| Nash 225
Natural topology 234
Nazareth 225
Neglecting covariances 31
Negligible, modelization uncertainties 34
Negligible, observational uncertainties 35
Neighborhood 231
NEP 12
Nercessian 144 289
Neumann series 238
Newton, algorithm 211
Newton, method 76 210
Newton, method (for -norms) 210
Noise additive 26
Noninformative probability density 11
Nonlinear least-squares 68
Nonlinear problem 64
Nonlinear regression 256
Norm 61 117 183 235
Norm, associated with exponential 3D covariance 313
Norm, associated with exponential covariance 308
Norm, associated with random walk 311
Norm, of a continuous operator 238
Norm, of the generalized Gaussian 250
Norm, of the gradient 209
Norm, properties 83
Norm, triangular 14
Normed linear space 235
Null space 184 238
Number, of iterations 69
Number, of parameters resolved 73
Objective function 64
Observable parameters 2
Observational uncertainties negligible 35
One-to-one 230
Onto 230
Open subset 231
Operator 230
Outlier 26 81
Outlier (example in geodetic adjustment) 296
Overdetermined 67
p-event 16
Pallaschke 225
Parameter manifold 6
Parameterization 1 2
Parameterization, equivalent 2
Parameterization, of a system 2
Parameters 6
Partial derivatives 68
Partition of data into subsets 197
Partitioned matrix inverse 250
Perfect information 9
Petrophysical parameters 24
Phillips 230
Physical, dimensions of a probability density 8
Physical, laws 2
Physical, system 1
Plackett 68
Point 232
Poisson ratio 163 166
Poisson ratio, homogeneous probability density 167
Poisson ratio, negative values 167
Polak 217
Popper 20
Positive definite bilinear form 240
Posterior covariance 66 70
Powell 203 217 219 220
Pre-Hilbert space 241
Preconditioned, gradient methods 78
Preconditioned, steepest descent 214
Prescribed covariance 116
Press 42
Principal components of the gradient 94
Prior probability density 32
probability 6
probability density 5 7 159
Probability density, a priori 32
Probability density, conditional 19
Probability density, homogeneous 7 10
Probability density, joint 19
Probability density, marginal 18
Probability density, noninformative 11
Probability density, physical dimensions 8
Probability density, theoretical 32
probability distribution 4
Probability, density 7
Probability, distribution 6
Probability, of causes 18
Probability, relative 7
Probability, volumetric 8
Probability-event 16
Product of probability densities 285
Pugachev 61 103 107 111 172
Quasi-Newton, algorithm 79
Quasi-Newton, in least squares 78
Quasi-Newton, method 69 215
Random exploration of the model space 38
Random walk, covariance function 114
Random walk, norm 311
Random, function 101
Random, function (characterization) 102
Random, function (realization) 111
Random, variable 9
Random, walk 52 102
RANGE 230
Rank of a linear operator 238
Rao 68 177
Rauhala 4
Reciprocity 146
Reeves 217
Reflexive space 239
Refutation of a theory 20
Rejection sampling method 49
Relative information (of two Gaussians) 201
Residuals large 74
Resolution operator 72
Resolving kernel 192
Ribiere 217
Richards 145 146
Riesz representation theorem 109 241
Rietsch 11 163
Roach 145
Roberts 229
Robust method 81
Rodgers 216
Rosenbrock function 204
Rothman 42 54
Roughing operator 61
Rounding error 81
Ruffle 41
Sample 6 34
Sampling, methods 48
Sampling, the posterior probability distribution 52
Sampling, the prior probability distribution 52
Savage 11
Scalar product 60 117 241 243
Scales 203 217 219
Schmitt 37
Schweizer 14
Self-adjoint 188
Self-adjoint operator 62
Self-adjoint, wave equation operator 190
Seneta 42
Sequential random realization 181
Sequential realization method 49
Series development 204
Shannon 12 220
shear modulus 11 165
Simplex method 95 96 223
Simplex method, example 293
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