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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 |
Linear function 6
Linear functional 79
Linear functional extension 80
Linear integral operator 62
Linear interpolant 395
Linear space 2
Linear system 208
Linear system, iterative method 208
Linearized elasticity 343
Linearly dependent 4
Linearly independent 4
Lipschitz constant 41
Lipschitz continuous 41
Lipschitz domain 279
Load vector 362
Local truncation error 266
Locally p-integrable 274
Lower semicontinuous (l.s.c.) function 130
Mapping 52
Mazur Lemma 133
meas(D) 15
Measurable function 16
Mesh parameter 400
Mesh refinement 408
Method of Lagrangian multiplier 438
Minimal angle condition 403
Minkowski inequality 44
Mixed formulation 352
Modulus of continuity 122
Monomial 38
Multi-index notation 38
Multiresotution analysis 193
Nekrasov's equation 212
Newton's method 230
Newton's method, convergence 231
Newton's method, Kantorovich theorem 232
Newton's method, nonlinear differential equation 234
Newton's method, nonlinear integral equation 233
Newton's method, nonlinear system 233
Node 390
Non-conforming element 386
Nonlinear equation 207 355
Nonlinear equation, Newton's method 230
Nonlinear equation, projection method 515
Nonlinear functional analysis 201
Nonlinear integral equation 233
Nonlinear operator, completely continuous 237
Nonlinear operator, derivatives 219
Nonlinear operator, Taylor approximation 237
Norm 8
Norm operator 57
Normed space 8
Normed space, reflexive 91
Numerical quadrature convergence 76
Nystroem method, asymptotic error formula 487
Nystroem method, collectively compact, operator approximation theory 489
Nystroem method, conditioning 488
Nystroem method, error analysis 481
Nystroem method, iteration method 505
Nystroem method, product integration 492
Obstacle problem 414
Open mapping theorem 73
Open set 10
Operator 52
Operator, addition 52
Operator, adjoint 85
Operator, bounded 54
Operator, closed 326
Operator, compact 93
Operator, compact linear 93
Operator, completely continuous 93
Operator, continuous 54
Operator, continuous linear 55
Operator, contractive 203
Operator, differentiation 53
Operator, extension 72 80
Operator, finite rank 95
Operator, linear 55
Operator, linear integral 62
Operator, Lipschitz continuous 203
Operator, non-expansive 203
Operator, norm 57
Operator, perturbation 66
Operator, projection 141
Operator, scalar multiplication 52
Operator, self-adjoint 87
Orthogonal 28
Orthogonal basis 28
Orthogonal projection 151 153
Orthonormal basis 28
Orthonormal system 28
Parallelogram law 24
PARAMETER 390
Parseval's equality 30
Petrov — Galerkin method 367
Petrov — Galerkin method, convergence 369
Picard iteration 204
Picard — Lindeloef theorem 215
Piecewise polynomial interpolation 121
Piecewise polynomial method 456
Poincare — Friedrichs inequality 297
Point evaluation 81
Poisson equation 324
Poisson ratio 345
Polarization identity 24
Polynomial approximation, relation to trigonometricolynomial approximation 154
Polynomial interpolation, barycentric formula 126
Polynomial interpolation, error formula 119
Polynomial invariance property 397
Primal formulation 348
Primal problem 351
Principle of uniform, boundedness 75
Product integration, error analysis 494
Product integration, graded mesh 498
Projection method 448
Projection method, conditioning 465
Projection method, error bound 454
| Projection method, finite problem 520
Projection method, homotopy argument 518
Projection method, iterated 468
Projection method, theory 451
Projection on closed convex set 141
Projection operator 150
Projection operator on closed convex set 141
Projection, interpolation 152
Projection, orthogonal 151
Quasiuniform triangulation 403
RANGE 52
Reference element 388
Reference element technique 384 399
Reference element, rectangular 388
Reference element, triangular 388
Reflexive normed space 91
Regularity condition 387
Regularization technique 436
Resolvent operator 107
Resolvent set 107
Riesz representation theorem 82
Ritz method 363
Ritz — Galerkin method 363
Rotation 518
Rotation of a completely continuous vector field 238
Saddle point problem 349
Scaling equation 195
Schauder basis 13
Schauder's fixed-point theorem 237
Scheme, backward 251
Scheme, backward-time, centered-space 251
Scheme, Crank — Nicolson 252
Scheme, forward 251
Scheme, forward-time, centered-space 251
Scheme, generalized mid-point 271
Scheme, Lax — Wendroff 255
Scheme, two-level 266
Schwarz inequality 22
Semi-norm 8
Separable space 13
Signorini problem 424
Simpson's rule 318
Sine integral function 168
Single layer potential 534
Single layer potential, evaluation 544
Singular elements 408
Smooth test function 324
Sobolev quotient space 298
Sobolev space 18
Sobolev space of integer order 280
Sobolev space of real order 286
Sobolev space over boundary 288
Sobolev space, compact embedding 292
Sobolev space, density result 290
Sobolev space, dual 309
Sobolev space, embedding 291 310
Sobolev space, extension 291
Sobolev space, Fourier transform characterization 303
Sobolev space, norm equivalence theorem 294
Sobolev space, periodic 307
Sobolev space, trace 293
Solution operator 256
SOR method 210
Space of continuously differentiable functions 38
span 5
Spectral method 457
Spectral radius 209
Spectrum 107
Spectrum, continuous 108
Spectrum, point 108
Spectrum, residual 108
Spherical harmonics 105 314
Spherical polynomial 313
Stability 67 262
Stability estimate 327
Stable 74
Stiffness matrix 362
Stiffness matrix, condition number 403
Stokes equations 353
Stone — Weierstrass theorem 114
Strain tensor 343
Stress tensor 343
Strictly convex function 129
Strictly normed space 137
Strong convergence 90
Strongly monotone 327
Sublinear 81
Sublinear functional 81
subspace 3
Superconvergence 475
Surjective 53
Transformation 52
Trapezoidal rule 311
Triangle inequality 8
Triangulation 387
Trigonometric interpolation 124
Trigonometric interpolation, convergence 158
Uniform error bound 154
Unstable 74
Urysohn integral equation 211
Vector space 2
Volterra integral equation 212
Volterra integral equation, second kind 64
Wavelets 185
Wavelets, Daubechies 197
Wavelets, Haar 185
Weak convergence 90
Weak derivative 274
Weak formulation 325
Weakly closed set 130
Weakly lower semicontinuous, (w.l.s.c.) function 130
Weakly sequentially lower semicontinuous function 130
Weierstrass theorem 114
Well-conditioned 74
Well-posed 74 256
Young's inequality 43
Young's inequality, modified 44
Young's modulus 345
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