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Bellman R. — Methods of nonlinear analysis (Vol. 2)
Bellman R. — Methods of nonlinear analysis (Vol. 2)



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Название: Methods of nonlinear analysis (Vol. 2)

Автор: Bellman R.

Аннотация:

This is the second of two volumes written to introduce the reader to some of the theories and methods which enable us to penetrate carefully and timorously into the nonlinear domain. Fortunately, we have no choice: the only direction is forward. In Volume I we focused on the basic concepts of stability and variational analysis and the analytic techniques required for their use such as linear differential equations and matrix analysis.
In this volume we wish to describe some newer approaches such as duality techniques, differential inequalities, quasilinearization, dynamic programming, and invariant imbedding as well as some older methods which have become operational, and thus of greater analytic interest, as a consequence of the development of the digital computer: iteration, infinite systems of differential equations, and differential and integral quadrature. Using these theories we shall be able to present a more satisfactory explanation of various phenomena noted in Volume I, and indicate some promising new techniques.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1970

Количество страниц: 261

Добавлена в каталог: 03.02.2006

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abel integral equations      248
Abel — Schroeder equation      183
Abel — Schroeder functional equation      157
Abel, J.M.      218
Abelian results      224
Aczel, J.      78
Adaptive polygonal approximation      101
Adaptive processes      78
Age-dependent stochastic branching processes      153
Aggregation      113
Almost-periodic coefficients      218
Ambarzumian, V.A.      153
Analytic continuation      153
Angel, E.      115 252 253
Aoki, M.      113
Approximate convex functions      46
Approximation in policy space      81 99
Arithmetic operations      180
Arley, N.      220
Asymptotic behavior      59 135 140 161
Asymptotic phase      138 140
Azen, S.      216 217
Beckenbach, E.F.      46 71
Bellman equation      112
Bellman functions      112
Bellman, R.      16 17 19 31 39 46—49 71—74 104 108 110—113 115 140 143 152—154 165 179 183 187—190 216 217 219 220 229 237 245 247 252—254
Beyer, W.A.      140
Bihari, I.      47
Birkhoff, G.      220
Birth-and-death process      219
Bocher, M.      42
Bochner, S.      48
Boltyanski, V.G.      112
Boltzmann equation      251
Bolza, O.      110
Borchsenius, V.      220
Branching processes      153 178 179 188 190
Bremmer series      142
Browder, F.E.      114
Brown, T.      111 154
Burgers’ equation      217 250
Calculus of variations      83 112 114
Calogero, F.      73
Caplygin, S.A.      47
Caplygin’s method      21
Carleman linearization      217
Carre, B.A.      111
Casti, J.      245 253
Celestial mechanics      188
Chandrasekhar, S.      153 253
Chang, S. Spital-Yo      183
Cheprasov, V.P.      112
Cherry, I.      216
Closure      214 219 220
Closure of operations      179
Cohen, D.S.      48
Coles, W.J.      74
Collatz, L.      46 73
Collins, D.C.      115
Collision interaction      152
Companion functional      4
Complex inversion formula      224
Computational aspects      120
Computational feasibility      67 91 93
Conditional Markov processes      114
Conjugate convex functions      19
Conservation law      70
Conservation relation      133
Constraints      95
Control processes      19 108
Convex functions      20
Cooke, K.L.      49 111 113 183 216 217 252
Corduneanu, C.      47
Cosmic rays      153
Cost, T.L.      248
Cox, D.R.      220
Cox, H.      113
Curse of dimensionality      95
Decision process      81
Deferred corrections      252
Devooght, J.      113
Difference methods      192
Differential inequalities      21
Differential quadrature      244 246 253
Diliberto, S.      188
Dimensionality      115
Dini’s theorem      54 73
Doetsch, G.      252
Dolph, C.L.      220
Dreyfus, S.E.      112 115
Duality      1 20
Duffin, R.J.      19
Durling, A.E.      115
Dynamic programming      75
Elliptic equations      69
Energy inequalities      34
Envelope of tangents      84
Error analysis      243
Erugin, N.P.      48
Esogbue, A.O.      115
Euclidean algorithm      152
Euler equation      85
Factorization      39 43
Factorization of the operator      26
Fatou, L.      183
Fejer sum      202
Feller, W.      219
Fel’dbaum, A.A.      114
Fenchel transform      17
Finite element method      251
Firing of nerves      186
Fleming, W.      114
Fortet, R.      250
Fox, C.      253
Froman, N.      113
Froman, P.O.      113
Fuller, A.T.      112
Functional equations      78 106 117 153 187
Fundamental inequalities      45
Fundamental lemma      23 47
Furstenberg, H.      189
Gabasov, R.      19
Generalized solutions      113
Geometric aspects      7 13
George, J.H.      48
Gershwin, S.B.      112
Gilleman, A.      19
Girsanov, I.V.      112
Glicksberg, I.      19
Gluss, B.      114
Green, J.W.      46
Green’s function      109 111
Grevy, A.      189
Gross, O.      19
Gruschinske, J.      253
Hadamard variational formula      110
Hadamard, J.      188
Hamilton — Jacobi method      112
Hamilton — Jacobi — Bellman equation      112
Harris, T.E.      153 179 188
Hartman, P.      48
Heins, W.      19
Hille, E.      114
Hopf, E.      70 113 250
Hyers, D.H.      46
Identification problems      245
Ikebe, T.      16
Ill-conditioned systems      75 101
Ill-conditioning      231
Imbedding      113 166
Imbedding technique      79 237
Improperly posed problems      252
Inequalities      18 46 71
Infinite stage process      80
Infinite systems      199 204 219
Internal fluxes      134
Interpolation technique      225
Invariant imbedding      240
Invariants      174
Inverse problem      110
Ioffe, A.      20
Iteration      156
Ja Pan, V.      190
Janossy, L.      153
John, F.      48
Johnson, C.D.      19
Jones, G.S.      45
Kachurovskii, R.I.      47
Kagiwada, H.      153 253 254
Kakicev, V.A.      253
Kalaba, R.      73 114 143 152—154 217 229 247 252—254
Kantorovich, L.V.      73
Karlin, S.      73
Karush, W.      17
Kashef, B.      104 253 254
Kato, H.      190
Kato, T.      16
Keller, H.B.      251
Keller, J.      69
Kendall, D.G.      190
Kesten, H.      189
Koenigs, G.      189
Koenig’s representation      158
Kolodner, I.I.      154
Krasnoselskii, M.A.      47
Krillova, F.M.      19
Kronecker matrices      164
Krotov functions      112
Kushner, H.J.      114
Ladas, G.      49
Lakshmikantham, V.      39 47 49
Lanczos, C.      251
Langenhops, C.E.      47
Laplace transform      221 252
Laptinskii, V.N.      47
Larson, R.E.      115
LaSalle, J.P.      48
Lattes, R.      252
Lavrientiev, A.      252
Lax, P.      70
Leau, L.      189
Leavitt, L.C.      220
Lee, E.B.      112
Leela, S.      39 47
Lefschetz, S.      48
Legendre polynomials      228
Lehman, S.      112 153
Levenberg, K.      249 253
Levinson, N.      179
Levitin, E.S.      72
Lew, A.      115
Lewis, D.C.      220
Limit theorems      111
Linear systems      127
Lions, J.      252
Liouville approximations      141
Liouville — Neumann series      153
List, S.E.      252
Localization principles      143
Lockett, J.      111 114 229 247 252
Locus of points      84
Lyapunov functions      36 48
Lyapunov’s second method      21
Majorization      159
Mangasarian, O.L.      47
Markovian optimization problems      114
Markus, L.      112
Maximum interval of convergence      54 64
Maximum principle of Pontrjagin      112
Maximum principles      46
Maximum transform      17 18 180
Mellin transform      248
Miller, H.D.      220
Miller, K.S.      112
Miller, R.F.      253
Minakshisundaram, S.      220
minimax      19
Minkowski’s inequality      71
Minty, G.J.      114
Mitter, S.K.      19
Mlak, W.      73
Mode, C.      188
Modified truncation      203
Moment behavior      165
Moment properties      219
Monotone convergence      52
Monotone operator equations      114
Monotone operators      21 46
Monotonicity of maximum      36
Moreau, J.J.      20
Mosco, U.      49
Moser, J.      48 73
Motzkin, T.      220
Multistage decision processes      77
Multistage processes      76
Nearest neighbor      103
Neutron transport theory      152
Newton — Raphson — Kantorovich approximation      54
Noh, W.F.      113
Nonlinear summability      238
Nonnegativity      31
Numerical inversion      229
Oguztoreli, M.N.      220
Ortega, J.M.      73
Orthonormal expansion      199
Osborn, H.      110 113
Ostrowski, A.      190
Pade approximation      248
Parabolic equations      69 220
Parabolic partial differential equation      31 44
Partial differential equations      195 245 250 252 253
Partial discretization      197
Particle counting      123
Particle processes      154
Pavlov, V.G.      112
Pereyra, V.      251 252
Perturbation analysis      124
Phase shifts      73 154
Philips, D.L.      252
Philips, R.      114
Physical solutions      227
Point of regeneration      153
Policy      81
Poljak, B.T.      72
Polygonal functions      15
Positive kernels      48
Positive operators      73
Positive solutions      47 48
Post — Widder inversion formula      247
Post, K.A.      185
Preisendorfer, R.      153
Prestrud, M.      153 253
Principe des r6duites      208 212 216 218
Principle of invariance      153
Principle of localization      144
Principle of optimality      86 87
Projective metrics      111
Property W      39 41 43
Protter, M.H.      113
Quadratic convergence      55 65
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