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Электронная библиотека Попечительского совета механико-математического факультета Московского государственного университета
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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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