Allaire G. — Numerical Analysis and Optimization: An Introduction to Mathematical Modelling and Numerical Simulation :: Электронная библиотека попечительского совета мехмата МГУ

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Allaire G. — Numerical Analysis and Optimization: An Introduction to Mathematical Modelling and Numerical Simulation

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Название: Numerical Analysis and Optimization: An Introduction to Mathematical Modelling and Numerical Simulation

Автор: Allaire G.

Аннотация:

This text, based on the author's teaching at Ecole Polytechnique, introduces the reader to the world of mathematical modelling and numerical simulation. Covering the finite difference method; variational formulation of elliptic problems; Sobolev spaces; elliptical problems; the finite element method; Eigenvalue problems; evolution problems; optimality conditions and algorithms and methods of operational research, and including a several exercises throughout, this is an ideal text for advanced undergraduate students and graduates in applied mathematics, engineering, computer science, and the physical sciences.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2007

Количество страниц: 455

Добавлена в каталог: 03.02.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$\alpha$ -convexity      290
Accuracy      35
Active constraint      312
Adjoint      209
Adjoint state      327
Admissible directions      306
Admissible solutions      350
Affectation      370
Alternating directions      50
Arcs      368
Banach space      81
Banded matrix      420
Basic solution      351
Basis      351
Bellman equation      372
Boundary value problem      25 67
Bounded support      68 87
Bramble — Hilbert lemma      189
Calculus of variations      283
Capacity      368
Cauchy problem      26 67
Cea’s lemma      151
Centred      15
CFL condition      19 24 40 47 267 272
Cholesky factorization      418
Circuit      372
Coercive      74
Compact      209 210
Compact support      80
Complementary energy      324
Complementary slack      361
complete      399
Complete graph      384
complexity      396 421
Condition number      409
Conjugate gradient      335 429
Conjugate gradient method      428
Connected      381
Connected components      381
Consistency      35
Constraint qualifications      312
Control      284 330
Convex      289 399
Convex envelope      362
Cost      368
Cost or objective function      284
Degrees of freedom      176
Differentiability in the sense of Frechet      298
Differentiability in the sense of Gateaux      300
Diffusion equation      2 5
Diffusive      57 274
Direct method      406
Dirichlet boundary condition      4
Discrete norm      166
Dispersive      57
distribution      105
Divergence      3
Domain of a convex function      391
Domain of dependence      10 263
Dual      358 402
Dual problem      320
Dynamic programming      372
Edges      381
Eigenfunction      214
Eigenmode      221
Eigenvalue      209
Eigenvector      209
Elasticity      12 136
Elliptic      28 74
Energy equality      71 242
Energy estimate      113 119 141 237
Energy space      84 236 242 246 251
Epigraph      290
Equipartition of energy      263
Equivalent equation      55
Euler inequality      303
Explicit      16
Extremal point      362
Farkas lemma      313
Finite differences      14
Finite velocity of propagation      8 10
Flow      368
Ford — Bellman algorithm      377
Forest      381
Fourier boundary condition      4
Function value      372
Gauss — Seidel method      427
Gaussian elimination      412
Givens — Householder method      438
Global minimum      285
Gradient      3 427
Gradient algorithm with fixed step      335
Gradient algorithm with optimal step      333
Gradient method      427
Greedy algorithm      380
Green’s formula      68 90
Green’s function      260
Heat flow equation      2
Hermite finite elements      169
Hilbert space      399
Hilbertian basis      400
Hyperbolic      28
Hyperplane of support      362 403
IMPLICIT      16
Infimum      285
Infinite at infinity      285
Initial condition      3
Integer envelope      364
Integer point      362
Integer polyhedron      364
Interpolation      159 186
Invariance under scale change      8
Irreversible      8
Iteration matrix      38
Iterative method      406
Jacobi method      426
Kirchoff law      368
Kruskal algorithm      381
Kuhn — Tucker theorem      319
Lagrange finite elements      176
Lagrange multiplier      305
Lagrangian      310 317
Lagrangian relaxation      391
lame      12
Lanczos method      442
Laplacian      3
Lattice      173 192
Lax — Milgram Theorem      74

Linear form      402
Linear programming      348
Linear scheme      37
Linear system      405
Local minimum      285
LU factorization      414
Mass matrix      225
Matrix assembly      178
Maximal solution      376
Maximum principle      8 20 38 127 165 255 262
mesh      14 153 171 191
Method of successive over-relaxation      427
Minimax principle      216
Minimizing sequence      285
Minkowski theorem      362
Modelling      2 4 7 14 134 136 144 255 257
Multi-index      96
Multilevel schemes      33 44
N-rectangle      191
n-simplex      171
Navier — Stokes      144
Neumann boundary condition      4
Newton’s method      342
Node      172
nodes      368
Nonoriented graph      381
NP-complete (problems)      397
Numerical convergence      168
Numerical diffusion      57
Numerical integration      157
One-sided      16
Operational research      347
Operations research      278
Operator      402
Optimal command      326
Optimal solution      350
OR      347
Order of a PDE      28
Order of a scheme      35
Oriented graph      368
Orthogonal projection      399
Outward normal      68
Parabolic      28
Partial differential equations      1
Path      372
Peclet number      6
Penalization      341 358
Periodic boundary conditions      39
Plate equation      14 170
Poincare inequality      77 88
Polyhedral      171
Polyhedron      171 350
Polynomial      396
Positive definite      209
Power method      436
Primal      358
Primal problem      320
Principle of virtual work      71 141
Problem relaxed      362
Projected gradient      337
Propagation at finite velocity      257 263
Quadrature      157
Qualified constraint      312 315
Rayleigh quotient      216
Rectangular finite elements      191
Regular mesh      185
Regular open set      69
Regularity      129
Regularizing effect      261
Rellich theorem      94
Reversible      8 10 60 261
Rigid body motion      139
Robin boundary condition      4
Saddle point      317
Schroedinger’s equation      12
Second derivative      302
Self-adjoint      209
Separable      401
Simplex algorithm      353
Singularity      133
Slack variable      349
Sobolev space      84
Space step, time step      14
Sparse matrix      421
Spectral decomposition      211
Spectral problem      214
Splitting      50
Stable      18 37 267
State      372
Steady      11
Stencil      34
Stiff      268
Stiffness matrix      149 151 156 225
Stokes      13 144
Strict convexity      290
Strong convexity      290
Strong solution      66
Subdifferential      392
Subgradients      392
Subordinate norm      406
Supergradient algorithm      393
Surface measure      68
system      12
Test function      71
Trace theorem      90
Transmission      124
Transmission boundary conditions      124
Transport      279 368
TREE      381
Triangular finite elements      171
Triangulation      171
Truncation error      35
Uniform mesh      154
Unimodular      365
Unisolvant      173 192
Unstable      18
Upwind      16
Uzawa’s algorithm      338
Valuation      379
Variational formulation      71
Variational solution      113
Vertices      154 381
von Neumann      41 45 272
Wave equation      9
Weak convergence      293
Weak derivative      81
Weak formulation      113
Weak solution      113
Well-posed      26

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