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Buhmann M.D. — Radial Basis Functions : Theory and Implementations
Buhmann M.D. — Radial Basis Functions : Theory and Implementations



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Название: Radial Basis Functions : Theory and Implementations

Автор: Buhmann M.D.

Аннотация:

It is necessary to estimate parameters by approximation and interpolation in many areas-from computer graphics to inverse methods to signal processing. Radial basis functions are modern, powerful tools which are being used more widely as the limitations of other methods become apparent. Martin Buhmann provides a complete analysis of radial basic functions from the theoretical and practical implementation viewpoints. He also includes a comprehensive bibliography.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 270

Добавлена в каталог: 09.07.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\Gamma$-function      133 151f.
Abelian theorem      83
Additional conditions on the rbf      59
applications      5f.
Approximate Lagrange functions      169
Approximation order      48 99 200
Approximation order of least squares      200
B-spline      17f. 43
Bernstein — Widder representation      13
Bessel function      26 152
BFGP algorithm      167
Bochner's theorem      155
Boundary value problems      30
Box-splines      42
Bramble — Hilbert lemma      110
Cardinal function      27 51ff.
Cardinal grids      49
Centres      3
Clough — Tocher interpolant      42
Compactly supported rbf      147ff.
Complete monotonicity      12
Completely monotonic      101f.
Completion      113
Condition numbers      89 136ff.
Conditional positive definiteness      101
Cone condition      110
Conjugate gradient method      179 188
Convergence analysis      16ff. 65ff. 123ff.
Convergence of BFGP method      175
Convergence orders      see "Convergence analysis"
Delaunay triangulation      41
Discrete least squares      201
Divided difference      17
Doubling the convergence order      129
Dynamical system      34
Eigenvalues      136
Euclidean norm      3
Far field      185
Fast multipole method      183
Fast Wavelet Transform      217
FFT techniques      50
Fourier series      24
Fourier transform of L      61f.
Gram-matrix      207
grid      48
Hilbert space      108
Implementation of least squares      207
Infinite lattice      48
Inner product      107
Interpolation      2 23
Interpolation linear system      12
Interpolation matrix      12
Inverse multiquadrics      21
Iterative methods      164
Kernel      106
Krylov space      177
Krylov space method      178
Lagrange conditions      52
Lagrange form      23
Lagrange function      23 51
Least squares      196ff.
Level      212
Lipschitz-continuous boundary      110
Local Lagrange functions      169
Localness      58
Micchelli's theorem      14
Minimum norm interpolant      115 123
Modified point evaluation functional      113
MRA      214
Multiple monotonicity      86 149
Multiply monotonic functions      86
Multipole method      165 183
Multiquadric      4 11
Multiresolution      214
Multivariate difference      214
Native space      114
Near field      185
Neural networks      6 208
Nitsche trick      129
Nonsingularity      12
Nonsingularity results      100
Norms of matrices      89
Numerical stability      89
Paley — Wiener theorem      95
Parseval — Plancherel identity      119 242
Partial differential equations      29
Piecewise polynomials      41
Poisson summation formula      25
Polynomial interpolation      37
Polynomial reproduction      18 63f.
Powell — Sabin split      42
Power function      116 120f.
Preconditioning      188
Preconditioning method      166 188
Prewavelet      212 224 226
Quantitative analysis      136
Quasi-interpolation      16 17 72 133 221
refinement      220
Refinement equation      219
Reproducing kernel      108 119
Reproducing kernel Hilbert space      109
Reproducing kernel semi-Hilbert space      109
Required properties of the rbf      57
Riesz bases      221
Saturation orders      79 80 130
Scattered data interpolation      99
Schoenberg's theorem      13
Semi-inner product      105
Semi-norm      105 106
Shepard's method      45
Shift-invariant space      112
Shifted logarithm      104
Simple prewavelet      225
Smoothing methods      209
Sobolev embedding      106
Sobolev inequality      109
Sparse grids      49
Special prewavelet      226
Sphere      235
Strang and Fix conditions      73
Symbol      24 57
Tauberian theorem      82
Tensor product      45
Thin-plate spline      61 104
Toeplitz matrix      92 194
Track data      5
Triangulations      41
Uncertainty principle      143 145
Unified class of compactly supported rbf      162
Uniqueness      26
Unisolvency      107
Variational theory      105
Voronoi tessellation      41
Wavelet      209
Wavelet decompositions      211
Wendland's functions      150
Whitney extension theorem      124
Wiener algebra      25
Wiener's lemma      24
Williamson representation theorem      86
Young's inequality      128
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