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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.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1970Количество страниц: 261Добавлена в каталог: 03.02.2006Операции: Положить на полку |
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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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