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Atkinson K.E., Han W. — Theoretical Numerical Analysis: A Functional Analysis Framework

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Название: Theoretical Numerical Analysis: A Functional Analysis Framework

Авторы: Atkinson K.E., Han W.

Аннотация:

This textbook covers basic results of functional analysis and also some additional topics which are needed in theoretical numerical analysis. For this second edition, a new chapter on Fourier analysis and wavelets and over 140 new exercises have been added, almost doubling the exercise amount from the last edition. Many sections from the first edition have been revised. Some of the other topics covered in this book are functional analysis and approximation theory, nonlinear analysis, Sobolev spaces, elliptic boundary value problems and variational inequalities.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2nd edition

Год издания: 2007

Количество страниц: 576

Добавлена в каталог: 10.06.2008

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Предметный указатель

$B(\cdot, r)$       10
$C(\bar{\Omega})$       3
$C(\Omega)$       2
domain      279
$C^k_p(2\pi)$       3
$C^m(\bar{\Omega})$       3 40
$C^m(\Omega)$       3 40
$C^{m, \beta}(\bar{\Omega})$       41
$C^{\infty}(\bar{\Omega})$       40
$C^{\infty}(\Omega)$       40
$C^{\infty}_0(\Omega)$       40
$C_p(2\pi)$       3
$H^k(\Omega)$       281
$H^k(\Omega)$ , inner product      282
$H^k_0(\Omega)$       286
      27
$H^s(2\pi)$       307
$H^s(\Omega)$       286
$H^s(\Omega)$ , inner product      286
$H^s(\partial \Omega)$       288
$H^s_0(\Omega)$       287
$H^{-1}(\Omega)$       287
$L^p(\Omega)$       43
$L^p_w(\Omega)$       18
$L^{\infty}_w(\Omega)$       18
$r_{\sigma}(B)$       58
$W^{k,p}(\Omega)$       280
$W^{k,p}(\Omega)$ norm      281
$W^{k,p}(\Omega)$ seminorm      281
$W^{m,p}(a,b)$       18
$W^{s,p}(\Omega)$       286
$W^{s,p}(\Omega)$ norm      286
$W^{s,p}(\partial \Omega)$       288
$W_0^{k, p}(\Omega)$       286
$W_0^{s, p}(\Omega)$       287
$\mathcal{L}(V, W)$       59
$\mathcal{P}_k$       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 $\delta$ -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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