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Авторизация |
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Atkinson K.E., Han W. — Theoretical Numerical Analysis: A Functional Analysis Framework |
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Предметный указатель |
10
3
2
domain 279
3
3 40
3 40
41
40
40
40
3
281
, inner product 282
286
27
307
286
, inner product 286
288
287
287
43
18
18
58
280
norm 281
seminorm 281
18
286
norm 286
288
286
287
59
6
A posteriori error estimate 438
a.e. 16
Abel integral operator 106
Abstract interpolation problem 116
Arzela — Ascoli theorem 48
Associated Legendre function 315
Aubin — Nitsche Lemma 406
Babuska — Brezzi condition 369
Backward triangle inequality 10
Banach fixed-point theorem 202 203
Banach space 14
Banach — Steinhaus theorem 75
Barycentric coordinates 389
Basis 5 391
Basis, countably-infinite 13
Basis, orthogonal 28
Basis, orthonormal 28
Basis, Schauder 13
Bessel's inequality 29
Best approximation 129
Best approximation, existence 134
Best approximation, inner product space 139
Best approximation, trigonometric polynomial 137 144
Best approximation, uniqueness 136
Best constant 302 303
Best uniform approximation 135
Bidual 91
Biharmonic equation 343
Bijection 53
Boundary integral equation 523
Boundary integral equation, direct type 531
Boundary integral equation, first kind 549
Boundary integral equation, indirect type 534
Boundary integral equation, numerical, first kind 551
Boundary integral equation, numerical, second kind 537
Boundary integral equation, second kind 537
Boundary value problem, Adler 341
Boundary value problem, homogeneous Dirichlet 334
Boundary value problem, linearized elasticity 343
Boundary value problem, Neumann 337
Boundary value problem, non-homogeneous Dirichlet 335
Boundary value problem, Robin 341
Brouwer's fixed-point theorem 236
Cartesian product 6
Cauchy sequence 13
Cea's inequality 366
Characteristic function 16
Chebyshev Equi-oscillation Theorem 136
Chebyshev polynomial 148
Closed operator 326
Closed range theorem 328
Closed set 10 130
Closed set, weakly 130
Collocation, iterated 472
Collocation, piecewise linear 457
Collocation, trigonometric polynomial 459
Compact linear operator 93
Compact operator 93
Compact operator, 97
Compact operator, C(D) 94
Compact operator, properties 95
Compact set 47
Compact support 40
Completely continuous vector fields 236 238
Completely continuous vector fields, rotation 238
Completion 15
Condensation technique 383
Condition number 74
Conjugate gradient iteration, convergence 240
Conjugate gradient iteration, superlinear convergence 241
Conjugate gradient method 239
Conjugate gradient method, operator equation 239
Conjugate gradient method, variational formulation 372
Consistency 67 259
Constitutive law 343
Continuity 10
Contractive mapping theorem 204
Convergence 10 262
Convergence order 264
Convergence, strong 90
Convergence, weak 90
Convergence, weak-* 92
Convex combination 129
Convex function 129
Convex function, strictly 129
Convex minimization 226
Convex minimization, Gateaux derivative 226
Convex set 129
Countably-infinite basis 13
Daubechies wavelets 197
Daubechies wavelets, scaling function 196
Degenerate kernel function 96
Dense set 12
Density argument 320
Derivatives, mean value theorems 223
Derivatives, properties 221
Difference, backward 250
Difference, centered 250
Difference, forward 250
Differential calculus 219
Differential equation Banach space 215
DIMENSION 5
Dirac -function 84
Dirichlet kernel function 156
Discrete Fourier Transform 181
Displacement 343
Displacement, normal 417
Displacement, tangential 418
Divergence theorem 525
Domain operator 52
Domain, spatial 38
Double layer potential 534
Double layer potential, evaluation 540
| Dual problem 351
Dual space 79
Dyadic interval 187
Dyadic number 186
Eigenvalue 103
Eigenvector 103
Elastic plate problems 343
Elasticity tensor 344
Elasto-plastic torsion problem 423
Element 387
Elliptic variational inequality, first kind 420
Elliptic variational inequality, second kind 428
Epigraph 431
Equivalence class 16
Equivalent norms 11
Exterior Dirichlet problem 528 534
Exterior Neumann problem 529 532
Fast Fourier Transform 182
FFT 182
Finite difference method 249
Finite difference method, convergence 262
Finite difference method, explicit 251
Finite difference method, implicit 251
Finite difference method, stability 262
Finite element method 378
Finite element method, convergence 404
Finite element method, error estimate 404
Finite element method, h-p-version 378
Finite element method, h-version 378
Finite element method, p-version 378
Finite element space 393
Finite elements, affine-equivalent 391
Finite elements, regular family 400
First kind integral equation 549
Fixed point 201
Fourier coefficients 162
Fourier series 144 162
Fourier series, coefficients 162
Fourier series, complex form 163
Fourier series, partial sum 156
Fourier series, uniform error bound 157
Fourier transform, discrete 181
Frechet derivative 219
Frechet differentiable 220
Fredholm alternative theorem 99
frequency 162
Frictional contact problem 416
Fubini's theorem 17
Functionals, linearly independent 116
Galerkin method 362
Galerkin method, convergence 366
Galerkin method, generalized 370
Galerkin method, iterated 470
Galerkin method, piecewise linear 461
Galerkin method, trigonometric polynomial 463
Galerkin method, uniform convergence 465
Gateaux derivative 219
Gateaux differentiable 221
Gauss — Seidel method 210
Generalization 64
Generalized Galerkin method 370
Generalized Lax — Milgram lemma 353
Generalized solution 257
Generalized variational lemma 274
Geometric series theorem 60
Gibbs phenomenon 167
Gram — Schmidt method 33
Green's first identity 526
Green's representation formula 526
Green's representation formula on exterior region 530
Green's second identity 526
Gronwall's inequality 218
Haar scaling spaces 187
Haar wavelet function 189
Haar wavelet spaces 189
Haar wavelets 185
Haar wavelets, scaling function 185
Hahn — Banach theorem 81
Hammerstein integral equation 212
Heat equation 250
Heine — Borel theorem 48
Helmholtz equation 334
Hermite finite element 390
Hermite polynomial, interpolation 121
Hilbert space 26
Hilbert — Schmidt integral operator 244
Hilbert — Schmidt kernel function 98
Hoelder continuous 41
Hoelder inequality 44
Hoelder space 41
Homotopy 238
Ill-conditioned 74
Ill-posed 74
Index of a fixed point 238
Inf-sup condition 369
Injective 53
Inner product 21
Integral equation 211
Integral equation, collocation method 448
Integral equation, Galerkin method 450
Integral equation, Hammerstein 212
Integral equation, iteration 212
Integral equation, nonlinear 211
Integral equation, Nystrom method 478
Integral equation, projection method 448
Integral equation, Urysohn 211 520
Integral equation, Volterra 212
Integral operator, Abel 106
Integral operator, self-adjoint 88
Integration by parts formula 319
Interior Dirichlet problem 524 531
Interior Neumann problem 524 531
Internal approximation method 370
Interpolation error estimate over the reference element 397
Interpolation error estimate, global 401
Interpolation error estimate, local 398
Interpolation operator 395
Interpolation projection 152
Interpolation property 45
Interpolation theory 115
Interpolatory projection 158
Invariant subspace 104
Isomorphic 6
Iteration method, integral equations 504
Iteration method, Laplace's equation 209
Iteration method, Nystroem method 505
Jackson's theorem 155
Jacobi method 210
Jacobi polynomial 146
Kelvin transformation 527
Korn's inequality 298
Krylov subspace 246
Lagrange basis functions 118
Lagrange finite element 390
Lagrange polynomial interpolation 117
Lagrange's formula 118
Lagrangian multiplier 438
Lame moduli 345
Laplace expansion 316
Lax equivalence theorem 262
Lax — Milgram lemma 331 332
Lax — Milgram Lemma, generalized 353
Lebesgue constant 157
Lebesgue dominated convergence theorem 17
Lebesgue integral 16
Lebesgue integration 15
Lebesgue measure 15
Legendre polynomial 34 146 315
Legendre polynomial, normalized 143
linear combination 4
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