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| Glasko V. — Inverse Problems of Mathematical Physics |
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| Предметный указатель |
Arzela's theorem 26
Bayes's theorem 35—37
Bolzano — Weierstrass theorem 15
Cauchy — Bunyakovskii inequality 75
Charged particle beam control 33
Consistency 22—24
Control problems 5—6
Control problems, charged particle beam 33
Control problems, induction tempering of steel 81—83
Control problems, stabilizer 31—34
Control problems, tempering 83—84
Correctness class 13—17
Correctness class, definition 15—16
Current amplitude 5
Defect detection 40
Dirichlet problem 57
Discrepancy principle 62—65
Earth's core 42
Earth's surface electromagnetic field 42—44
Earth's surface electromagnetic field, electromagnetic fields 13
Earth's surface electromagnetic field, gravitational fields 13 19
Elastic compression 46
EQUIVALENCE 45—47
Equivalence sets 31—34
Fourier series instability 9
Fourier series instability, potential 60
Frechet differential 70
Fredholm equation first kind 3 40—41
Fredholm, integral equation 7
Gauss — Newton iterations 83
Gauss — Newton procedure 69—70
Gravimetry 23 30 55—58
Gravitational field 19
hadamard 6
Hadamard problem 41 76
Heat conductivity 51—55
Heat conductivity, boundary value 51
Heat conductivity, locating source 52
Heat source intensity 40
Hilbert norm 24
Hilbert space 63—65
Hilbert space, stabilizer 33
Ill-posed problems, consequences 8—11
Impedance 45—46 48
Index of refraction 48
Induction 48
Induction, tempering of steel 81—83
Instrumental problems 3
Interpretation class, definition 22
Interpretation of physical observations 3
Inverse problems classes 1—11
Inverse problems classes, posing 13—37
Inverse problems classes, regularizing algorithms 59—88
Inverse problems classes, uniqueness 39—58
Iteration operators 80—81
Laplace transform 10
Layered media 42—50
Magneto-Telluric Sounding method 42—44
Minimization Euler equation 71—73
Minimization Euler equation, parametric functional 29
| Minimization Euler equation, smoothing potential 69—70
Newton's Laws 1 10
Optical covers 32
Optical filters 42
Optical systems 4
Parameter selection, quasi—optimal method 65—68
Parameter-descent method 68—69
Parametric functional, minimization 29
Picard's theorem 41
Practical equivalence set 21
Quasi-inversion operator 79—80
Quasi-minimization 22—23
Quasi-optimal method 65—68
Quasi-optimal method, definition 66—67
Quasi-solution 18—20
Quasi-solution, definition 18
Reflection coefficient 45—48
Regularization 20—34
Regularization principle 29
Regularization theory 11
Regularization, simplified 77—79
Regularization, statistical approach 35—37
Regularizing operator adaptive 60 73—81
Regularizing operator adaptive, definition 59
Regularizing operator adaptive, general 60 62—73
Regularizing operator adaptive, stochastically regularized 61 67
Regularizing operator adaptive, types 60—61
Resistance 48
Seismic waves 46
Seismic waves, dispersion 49—50
Seismic waves, Lyav wave 49—50
Seismology elastic waves 84—88
Seismology elastic waves, inverse kinematics 87—88
Seismology elastic waves, seismic prospecting 84—88
Seismology elastic waves, surface waves 85—86
Selection automatization 18
Shear waves 46
Sobolev Norm 24
Stability problem, regularizing operator 59—61
Stabilizer 24—27
Stabilizer, conditional 29
Stabilizer, control problems 31—34
Stabilizer, definition 24
Stabilizer, synthesis problems 31—34
Stabilizer, Tikhonov operator 83
Synthesis problems 4 6
Synthesis problems, optical systems 4
Synthesis problems, stabilizer 31—34
Tempering by induction 32
Tikhonov operator, consecutively stabilizing 83
Tikhonov — Cagniard method 42—44
Tikhonov's theorem 14—15
Transmission coefficient 4
Uniqueness interpetation 39
Uniqueness interpetation, linear correspondence operator 40—42
Volterra integral equation 7
Volterra integral equation, convolution type 40
Volterra, equation of the first kind 9
Well-posed problem consistency 22—24
Well-posed problem consistency, stabilizer 27—30
Well-posed problems 6—7
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