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Gershenfeld N. — The Nature of Mathematical Modelling-Neil Gershenfeld
Gershenfeld N. — The Nature of Mathematical Modelling-Neil Gershenfeld



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Название: The Nature of Mathematical Modelling-Neil Gershenfeld

Автор: Gershenfeld N.

Аннотация:

This book first covers exact and approximate analytical techniques (ordinary differential and difference equations, partial differential equations, variational principles, stochastic processes); numerical methods (finite differences for ODE's and PDE's, finite elements, cellular automata); model inference based on observations (function fitting, data transforms, network architectures, search techniques, density estimation); as well as the special role of time in modeling (filtering and state estimation, hidden Markov processes, linear and nonlinear time series). Each of the topics in the book would be the worthy subject of a dedicated text, but only by presenting the material in this way is it possible to make so much material accessible to so many people. Each chapter presents a concise summary of the core results in an area, providing an orientation to what they can (and cannot) do, enough background to use them to solve typical problems, and pointers to access the literature for particular applications.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 356

Добавлена в каталог: 17.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Minimum description length      2 115
Mixture models      175
Mixture of experts      178
ML      117
MLP      138
Mod map      207
Model errors      113 147
Molecular Dynamics      102
Moment generating function      49
Moment of inertia      41
Momentum      161
Monte — Carlo sampling      116
Moving average model      205
MPI      254
Multigrid methods      91
Multilayer perceptrons      138
Multistationary      153
Mutual information      218
NAG      227
NAR      208
Narrow-sense stationarity      51
Natural splines      141
Navier — Stokes equation      107
Nelder — Mead method      157
NETLIB      227
Neumann boundary conditions      84
Neural networks      150
Newton’s method      123
No free lunch theorem      113
Noether’s theorem      39
noise reduction      186
Nonlinear least squares      122
Nonparametric fitting      115
Nonuniform B-splines      141
Nonuniform rational B-splines      142
Normal distriibution      49
Normal modes      13
NullSpace      119
Numerical dissipation      81
Numerical quadrature      73
Numerical Recipes      227
NURBS      142
Nyquist frequency      130
o      18
Object oriented programming      245
ODE      9
One-sided Laplace transform      13
One-sided z-transform      19
Open Inventor      244
OpenGL      240
Operator splitting      84
Order of differential equation      9
Ordinary differential equation      7 9
Orthogonal functions      94 143
Orthogonal matrix      119 128
Orthogonal transformation      128
Orthogonal vectors      128
Orthonormal functions      143
Orthonormal vectors      128
OSI      250
Out-of-sample error      147
Outer product      136
Overfitting      147
Packet      250
Pade approximant      139
Parabolic PDE      27
Parametric fitting      115
Partial differential equation      7 9
Partial fraction expansion      14 15
Particular solution      10
Pattern recognition      184
PCA      137
PDE      9
PDF      231
Penalty function      154
Perceptrons      152
Periodic boundary condition      82
Pesin’s identity      219
Phase-locked loop, PLL      323
Point predictions      221
Poisson’s equation      27 84
Poles      15 206
Polynomial expansion      139
Port      251
Portable Document Format      231
Positive definite matrix      177
PostScript      230
Powell’s method      159
Power spectral density      50
Prediction      186
Predictor step      73
Predictor-corrector method      72
Principal axes      41
Principal components analysis      137
Printer’s point      231
Prior      47 116 154
probability density      169
probability distribution      7
Pseudo-inverse      119
Punctuated equilibrium      316
Q, quality factor      22 261
Quadrature mirror filter      133
Radial basis functions      146
Radial correlation function      214
Random variable      44
RANGE      119
Rank      119
Rational function      15
Rayleigh — Ritz method      93 100
RBF      146
Realization of stochastic process      45
Recurrent network      153
Recursion relation      59
Redundancy      218
Regularization      154
Relaxation technique      89
Representation      128
Residual      94 120
Richardson extrapolation      75
Rigid body motion      40
Schwarz’ inequality      187
Score      125
Second moment      46
Second-order Runge — Kutta method      70
Separation of variables      27
server      235
Shape functions      97
Sherman — Morrison formula      87
Shooting method      76
Short-Time Fourier Transform      131
Side-lobes      130
Signal separation      186
SIMD      107
simplex      157
Simulated annealing      163
Sine function      130
Singular value decomposition      119
Singular values      119
Smoothing      186
Snell’s law      270
Socket      251
Soft clustering      184
Solitons      65
Sonification      225
SOR      90
Source entropy      219
Spec      257
Spectral radius      89
Spin glass      167
Splines      98 141
Spread Spectrum      196
Spreadsheet      229
Standard deviation      46
State-space reconstruction      208
Stationary process      51
Steepest descent      123
STFT      131
Stiff differential equation      75
Stochastic processes      7 50
Stochasticity      44
Strange Attractor      217
Strict stationarity      51
Successive over-relaxation method      90
Support      45
Surrogate data      214
SVD      119
tar      208
TCP      251
threads      246
Time series analysis      204
TLA      137
Transfer function      17 206
TRANSPOSE      128
Transversality      211
Trellis      199
trending      205
Tridiagonal matrix      83
Two-sided Laplace transform      13
UDP      251
Uncorrected variables      47
Underfitting      147
Uniform Resource Locator      2
Unitary      128
Unreliable protocol      251
Unsupervised learning      175
Upper-diagonal matrix      83
URL      2
Vandermonde matrix      121
Vapnik — Chervonenkis dimension      148
Variable subset selection      137
Variance      46
Variational methods      7
VC      148
Vector quantization      185
Visualization      225
Viterbi algorithm      202
Volterra series      208
Von Neumann stability analysis      80
Voronoi tesselation      184
VRML      244
Wavelets      131
Weak stationarity      51
Weighted residuals      93
Whitney embedding theorem      211
Wide-sense stationarity      51
Wiener filter      186 187
Wiener process      54
Wiener — Hopf equation      189
Wiener — Khinchin theorem      51
Wigner function      136
Windowing      130
Wold decomposition      207
World Wide Web      2
X Windows      234
Yule — Walker equation      207
z-transform      19
zeros      15 206
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