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Baker G.A., Gammel J.L. — The Padé Approximant in Theoretical Physics
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Название: The Padé Approximant in Theoretical PhysicsАвторы: Baker G.A., Gammel J.L. Аннотация: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: 1Год издания: 1970Количество страниц: 378Добавлена в каталог: 18.04.2010Операции: Положить на полку |
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172 225 Abramowitz 259 273 277 257 Accelerating convergence of a sequence 139 Akhiezer, N. I. 198 201 206 212 216 217 Alexander 95 Amati, D. 341 342 567 Analytic structure of scattering amplitudes 231 241 257 313 336 Analytic tanget matrix 311 Arndt, R. A. 350 367 Aspnes, D. 33 39 Atkinson, D. 242 249 250 252 256 Axilrod 50 95 Baker, G. A., Jr 1 2 6 7 8 12 16 19 20 29 31 32 33 35 36 38 42 45 46 47 61 70 71 72 73 93 95 101 106 128 137 169 177 182 185 186 189 193 195 198 199 200 217 227 229 233 238 239 242 247 259 287 308 331 334 367 Ball, J. S. 233 231 239 Banach space 188 Bander, M 242 256 Barker, J. A. 62 82 83 84 95 Beach, J. Y. 76 Bederson, B. 63 80 96 Bell, R. J. 52 85 94 95 Bernstein, R. B. 41 78 78 79 79 81 82 95 Berstein, F. 38 Bessis, D. 197 217 219 229 305 331 349 364 365 367 Bethe — Salpeter equation 197 220 257 289 334 Bethe, H. A. 56 95 Binning of Monte Carlo integrands 339 Bird, R. B. 90 91 93 96 Bootstraps 241—242 249 256 Borel continuation 87 Borel transform 184 Born expansion 312 Bounded analytic functions reduced to series of Stieltjes 18 Bounded operators 172 Bounds, on averages, using moment constraints 99 Bounds, on estimates of interatomic interaction 47 49 Bounds, on refractive index 70—71 Bounds, on relativistic terms in atomic interactions 84 Bounds, on sums of series, in cut plane 12 Bounds, on sums of series, of Stieltjes 18 Bounds, on sums of series, on real axis 11 46 256 Bounds, on sums of series, provided by generalized Pad 25 Bounds, on thermodynamic quantities for Ising model 31 Bounds, on three-body dipole-dipole interaction 84 Breit, G. 333 367 Brooks, P. R. 81 Brown, L. 178 182 Buck, V. 79 Carleman’s criterion 11 202 Casimir — Polder formula 44 52 Casimir, H. B.G. 41 43 51 95 CDD poles 242 Chamberlain, G.E. 63 63 80 95 Chan, Y. 76 Chang, T. Y. 52 85 95 Chen, A. 197 217 Chew, G. F. 231 239 241 256 Chisholm, J. S. R. 8 35 36 38 174 176 178 179 180 182 307 331 334 335 367 Churchhill, R. V. 28 38 Cini 219 222 230 Cini — Fubini approximation 219 222 Clementi, E. 60 Coexistence curve 31 Common, A. K. 12 38 42 71 95 197 217 225 230 241 246 256 Compact operators 173 Complete continuity 173 209 Complete continuity, solution to integal equation with comletely continuous kernel 177 Construction of function which is difference of two series of Stieltjes from coefficients in power series expansion 36 137 Continued fractions 263 Continuous orthogonal expansions of Stieltjes transforms 131 Continuous orthogonal expansions of Stieltjes transforms, compared with Pad 134 153 162 Continuous orthogonal expansions of Stieltjes transforms, convergence of 132 Continuous orthogonal expansions of Stieltjes transforms, generalizations 134 Contogouris, A. 250 256 Convergence examples 260 327 330 Convergence examples, conjectures 19 Convergence examples, generalized 21 193 Convergence examples, in mean 254 Convergence examples, in measure 227 Convergence examples, theorems 189 151 Convergence examples, theorems for continuous orthogonal expansions 130 132 Convergence examples, theorems for matrix elements of resolvent of symmetric operator 206 212 Convergence examples, theorems for Pad 2 6—10 225 229 239 245 Cooper, J. W. 62 95 Copley, L. A. 197 218 Copson, E. 14 38 Coulomb scattering 285 Coupled channels 269 303 350 Critical exponents 32 Crowell, A. D. 90 91 95 Curtiss, C. F 90 91 93 96 Cutkosky, R.E. 343 367 Cziffra, P. 333 367 Dalgarno, A. 41 49 50 52 54 57 58 59 60 60 61 62 63 66 66 68 73 76 78 78 79 79 80 80 81 82 82 83 83 84 84 85 85 86 86 89 90 95 Davison, W. D. 41 49 50 62 63 76 78 79 80 81 84 85 89 95 de Montessus de Balloire, R. 10 38 Degges 73 Diagram representation of perturbation theory 146 Difference of two series of Stieltjes see Construction Diffusion by random velocity field 139 Dipole dispersion force coefficients for alkali atoms 79 Dipole dispersion force coefficients for alkali atoms for alkali atom-diatomic molecules 83 Dipole dispersion force coefficients for alkali atoms for atomic helium 76 Dipole dispersion force coefficients for alkali atoms for atomic hydrogen 76 Dipole dispersion force coefficients for alkali atoms for diatomic gases 80 Dipole dispersion force coefficients for alkali atoms for inert gas-alkali atom 81 Dipole dispersion force coefficients for alkali atoms for inert gas-alkali atom, -diatomic molecule 82 Dipole dispersion force coefficients for alkali atoms for inert gases 78 Dipole oscillator strength 43 Dipole-dipole contribution to atomic interactions 47 Direct interaction approximations 157 169 Dispersion force coefficient 43 86; Dispersion relations 232 Domain of convergence see convergence Domb, C. 30 38 Durin, R. 78 Dynamic dipole polarizability 44 Dyson equation for bubble propagator 297 Eisenbud, O. 304 332 Eisenschitz — London formula 43 Eisenschitz, R. 41 42 95 Electron-hydrogen scattering 285 Elias, D,K. 197 218 Energy spectrum function of velocity field 139 Epsilon algorithm 4 139 Epstein, S. 54 85 86 94 95 96 Error bounds see bounds Eve, J. 32 38 Faddeev equation 280 Faddeev, L.D. 280 287 Fano, U. 62 95 Feldman, D. 178 182 Feynman graph calculations 304 335 342 Fisher, M. E. 29 30 32 38 Fivel, D. I. 178 182 Fourier transform 183 Franklin, P. 26 38 Fredholm method 171 231 246 256 Free energy 31 115 Friedman, A. 188 195 Fubini, S. 219 222 230 Fubini’s Theorem 187—188 Fugacity 29—30 Functional analysis 171 Futrelle, R.P. 95 100 128 Gammel — Baker approximants see Generalized Pad Gammel, J. L. 19 35 38 197 218 239 239 304 331 Gargantini, J. 12 38 Gegenbauer polynomials 276 Generalized functions 184 Generalized functions of noncompact support 194 Generalized Pad 20 106 186 189 Generalized Pad 216 Generalized Pad 21 193 Generalized Pad 248 Gilbert, H. E. 32 38 Gill, P. 69 70 74 74 95 Glennon 66 66 97 Goldberger, M. L. 342 346 367 Gordon, R. G. 15 38 94 95 96 100 101 103 115 117 120 124 128 Goscinski, O. 94 96 Gotze, W. 33 39 Graben, H. W. 51 95 Graffi, S. 349 364 365 367 Grashin, A. F. 349 567 Grecchi, V. 349 364 365 367 Green’s function 140 Grisaru 342 346 367 Gronwall, T. H. 19 38 Guttinger, W. 183 184 186 193 Hadamard, J. 12 38 Hale, G. 318 331 Halmos, P. R. 227 230 Hamblen, D. 33 39 Hamburger moment problem see Moment problem Hamburger, H. 15 38 Hamilton, J. 299 302 Haracz, R. D. 342 367 Hardy, G.H. 18 38 114 128 Harmonic solid see Simple harmonic solid Harriman, J. 56 95 Haymaker, R. 258 272 273 279 287 Heat capacity of simple harmonic solid 115 121 Hecht, R 33 39 Heddle, D. W.O. 69 70 74 74 95 96 Heisenberg model 220 Helbing, R. 78 Helicity 291 Henrici, P. 12 38 39 Herglotz, G. 18 38 Hildebrand, F. B. 326 331 Hirschfelder, J. O. 41 51 76 90 91 93 96 Hoheisel, G. 171 172 173 177 182 Huckaby, D. 121 128 Hull, M. H., Jr 333 367 Hurst, R. P. 59 96 Inequalities obeyed by Pad 11 Integral equations 171 Internal energy of simple harmonic solid 115 Irreducible diagram expansion 129 156 Irreducible diagram expansion, condition for validity of certain manipulations on 169 Isenberg, C. 115 116 117 121 725 J-fraction 199 201 Jansen, L. 51 96 Jeffreys, B.S. 26 38 Jeffreys, H. 26 38 Jennings, R. E. 70 74 74 96 Jensen’s inequality for convex functions 114 Jensen’s inequality for convex functions, 303 Johnson, R. E. 85 86 95 Jones, C. E. 254 256 Kadanoff, L. P. 33 39 Kane, J. 33 39 Karlin, S. 100 111 128 Karplus 41 42 45 48 52 54 59 62 63 65 67 68 70 71 72 75 76 83 85 87 88 89 94 95 96 101 Kato 217 218 Kernels defined 172 Kernels defined, exact solution of integral equation with kernel of finite rank 176 Kernels defined, rank 174 Khanna, B. N. 69 70 74 96 Kihara 51 96 Kim, J. K. 331 Kingston, A. E. 52 54 61 62 74 80 82 83 84 85 95 Kirkwood, J.G. 75 90 96 Kirn, M 69 70 96 Koch, J. 70 96 Kohn variational principle 221 223 Kohn variational principle, convergence of 226 275 Kolker, H. J. 54 67 68 71 72 76 96 Kowalski, K. L. 178 182 289 302 Kraichnan, R. H. 134 144 157 169 169 Kramer, H. L. 93 96 Kramers — Heisenberg dispersion formula 42 44 Kramers — Heisenberg dispersion formula, 173 225 246 250 Kramers — Heisenberg dispersion formula, potential scattering kernel with Yukawa potentials is 181 Krein, M.G. 100 111 128 Kubis, J. J. 304 331 Kyle, H. L. 286 287 Landorff, R. W. 78 Langhoff, P. W. 41 42 45 48 54 59 62 63 63 65 70 75 83 85 87 88 89 94 96 101 Lassila, K. E. 333 567 Le Roy function 28 Leader, E. 341 342 567 Lee, B. W. 178 752 Lee, T. D. 29 30 31 59 Leighton, R. 116 117 725 Leonard, P. J. 62 82 83 84 95 Lepore, J. V. 334 567 Levine, M. J. 220 250 289 302 Levinger, J. S. 74 Lewis, E. A. S. 33 39 Liggett, G. 74 Linear integral equations 171 Lippman — Schwinger equation 178—179 197 220 221 Littlewood, J. E. 114 725 London formula 75 London, F. 41 42 75 88 91 95 96 Lowdin, P. O. 76 Lyth, D. H. 250 253 256 MacDowell, S. W. 342 346 367 MacGregor, M. H. 333 341 350 367 Machida, S. 334 367 Mandelstam, S. 231 259 241 256 344 567 Margenau, H. 75 88 96 Markov, A. 100 725 Martin, A. W. 241 242 256 Mason, E. A. 75 90 91 96 Mass operator of quantum field theory 147 Masson, D. 150 170 197 275 231 240 Mattioli, G. 335 567 Mavroyannis, C. 88 90 96 McDonald, F.A. 35 55 197 275 239 259 McDonald, J.R. 5 59 Mclnnis, B. C. 279 257 McQuarrie, D. A. 100 725 Meath, W. J. 41 51 85 56 96 Melton, L. A. 100 707 725 Method of moments for operators in Hilbert space 197 206 Method of moments for operators in Hilbert space, as generalized Pad 216 Method of moments for operators in Hilbert space, convergence for matrix elements of resolvent of symmetric operator 212 Method of moments for operators in Hilbert space, special perturbation technique 217 Metropolis, N. 341 567 Meyer L. 51 96 Mignaco, J. A. 305 552 Mikhlin, S. G. 171 752 Milne — Thompson, L. 16 59 Moiseiwitsch, B. L. 221 230 Moment problem 15 100 185—186 194 198—199 Moment problem, Carleman’s criterion for determinateness of 202 Moment problem, indeterminate case 216 Moment problem, Stieltjes inversion formula 199 Moments 100 101 108 185 264 Moments of oscillator strength distributions 45 53 Moments of oscillator strength distributions, determined from optical dispersion and absorption data for heavier atoms and molecules 60 Moments of oscillator strength distributions, for atomic helium 57 63 Moments of oscillator strength distributions, for atomic hydrogen 55 Monchick, L. 90 91 96 Monte Carlo integration 337 Moore, C. E. 66 66 96 Moravcsik, M. J. 333 341 350 567 Morrison, I. H. 75 79 80 85 55 86 56 90 95
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