Jetter K. (Ed), Schaback R. (Ed) — Topics in Multivariate Approximation and Interpolation :: Электронная библиотека попечительского совета мехмата МГУ

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Jetter K. (Ed), Schaback R. (Ed) — Topics in Multivariate Approximation and Interpolation

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Название: Topics in Multivariate Approximation and Interpolation

Авторы: Jetter K. (Ed), Schaback R. (Ed)

Аннотация:

This book is a collection of eleven articles, written by leading experts and dealing with special topics in Multivariate Approximation and Interpolation. The material discussed here has far-reaching applications in many areas of Applied Mathematics, such as in Computer Aided Geometric Design, in Mathematical Modelling, in Signal and Image Processing and in Machine Learning, to mention a few. The book aims at giving a comprehensive information leading the reader from the fundamental notions and results of each field to the forefront of research. It is an ideal and up-to-date introduction for graduate students specializing in these topics, and for researchers in universities and in industry.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 346

Добавлена в каталог: 22.05.2008

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Предметный указатель

$\Gamma$ -representation      213
Admissible      293 326
Admissible, *-admissible      327
Admissible, *-q-admissible      332
Admissible, p-admissible      332
Algorithm, $\nu$ -SVM      285
Algorithm, Chaikin      34
Algorithm, classification      275
Algorithm, corner cutting      137
Algorithm, de Boor      135
Algorithm, de Casteljau      134
Algorithm, Doo-Sabin      173
Algorithm, learning, ERM      258 260
Algorithm, learning, multi-task      284
Algorithm, learning, online      285
Algorithm, tree-based      240
Antilinearity      333
Approximation error      42 265
Approximation order      43
Approximation with regularization      86
Approximation, least square      86
Basis of an ideal      213
Basis, $\Gamma$ -basis      213
Basis, B-spline      136
Basis, B-spline like      136
Basis, Bernstein      133
Basis, Bernstein-like      117
Basis, Bernstein-like, piecewise      144
Basis, biorthogonal      89
Basis, dual      89
Basis, Groebner basis      213
Basis, H-basis      213
Basis, hierarchical      70 93
Basis, homogeneous      218
Basis, Newton      203
Basis, Riesz      88
Basis, wavelet      88
Bayes rule      275
Bessel property      294
Bezier points      126
BHS      51
Blossom      126
Blossom for polynomials      131
Cancellation property      88
Central surface      180
Characteristic map      164
Characteristic map, complex      169
Characteristic map, normalized      165
Classifier, associated with RKHS      276
Classifier, binary      275
Classifier, support vector machine      276
Classifier, SVM, hard margin      276
Classifier, SVM, q-norm soft margin      278
Classifier, SVM, soft margin      277
Coherent state      292
Coherent state from a unitary representation      293
Commuting property      329
Complete monotonicity      5
Condition number      238
Consistency condition      152
Control point      133 158
Coordinate system, local      179
Covering number      261
Covering number, -empirical      264
Cross validation      95
Cross validation, generalized      95
Cross validation, generalized, multilevel version of      96
Cross validation, potential      95
Cross validation, potential, multilevel version of      95
Curvature continuity, non-trivial      177
Curvature continuity, trivial      177
Data compression      92
Data fidelity term      86
Data, generic      164
DFT      168
Difference, divided      207
Difference, divided, multivariate      204
Difference, finite      203
Difference, forward      5
Dimension, $V_{\gamma}$ dimension      264
Distance, fill      237
Distance, Hausdorff      42
Distance, separation      237
Distribution, conditional      258
Distribution, marginal      258
Domain decomposition      241
Edge, convex      28
Edge, straight      28
Eigencoefficient      163
Eigenfunction      163
Eigenfunction, subsubdominant      178
Eigenvalue, subdominant      163
Eigenvalue, subsubdominant      177
Eigenvector, ineffective      160
ENO      29
ENO, weighted      31
Entropy, maximum discrimination      285
Entropy, metric      264
ERM      258
Error sample      260
Error, $\phi$ -error      279
Error, $\phi$ -error, empirical      279
Error, approximation      42 265
Error, empirical      259 260
Error, empirical, minimization of      260
Error, empirical, penalized      268
Error, ERM decomposition      260
Error, excess generalization      269
Error, generalization      259
Error, misclassification      275
Error, regularization      269
Error, regularization, decomposition      270
Evaluation point      239
Expansion, far field      239
Expansion, multipole      239
Exponent, separation      282
Exponent, Tsybakov's noise      282
Exponent, variancing      271 280
Extraordinary point      150
Feature selection      284
Fourier index      168
Fourier transform      234
Fourier transform, discrete      168
FSI      58
Function, $\psi$ -regression      265
Function, central height      154
Function, classifying loss      278
Function, conditionally positive definite      236
Function, empirical target      260
Function, harmonic      101
Function, Hilbert      217
Function, Hilbert, affine      218
Function, Hilbert, homogeneous      217
Function, Lipschitz      262
Function, loss      258
Function, nodal      68
Function, piecewise      137
Function, piecewise       138
Function, refinable      58
Function, regressing loss      259
Function, regression      258
Function, regularizing      269
Function, scaling      88
Function, target      260
FVS      76
Gauss map      154
GCV      95
Generator      57
Generator for p(G)      316
Generator, linearly independent      58

Generator, linearly independent, locally      58
Generator, linearly independent, over a set      58
Generator, local      58
Generator, refinable      58
Generator, stable      58
Generator, symmetric      65
Geometric characterization      199
Grading      210
Grading, monomial      212
Grading, Newton basis for      218
Grading, strict      212
Haar measure      299
Haar measure for $SU_{1,1}$       300
Half domain      170
Half segment      170
Hyperplane in general position      200
Hyperplane, optimal      277
Ideal      212
Ideal, basis of      213
Ideal, generated by F      213
Ideal, homogeneous      213
Ideal, monomial      213
Inequality, Bernstein      13 14 261
Inequality, Hoeffding      261
Inequality, Jackson — Favard      16
Inequality, probability      260
Inner product, native      235
Integral representation, Koornwinder's      8
Integral representation, Laplace      9
Interpolation with multiplicities      195
Interpolation, cubic spline      40
Interpolation, almost poisedness of      197
Interpolation, BHS scheme      51
Interpolation, correct for P      194
Interpolation, geometric      50
Interpolation, Hermite      47 114 195
Interpolation, Hermite — Birkhoff      195
Interpolation, Hermite, cubic two-point      47
Interpolation, Hermite, piecewise      140
Interpolation, Hermite, quintic two-point      48
Interpolation, ideal      195
Interpolation, Lagrange      195
Interpolation, poised for P      194
Interpolation, polynomial      194
Interpolation, Taylor      113
Irreducibility      308
Jacobi weight      3
Jacobian determinant      164
K-functional      17 267
Kernel, conditionally positive definite      236
Kernel, Gaussian      264
Kernel, Mercer      268
Kernel, radial      234
Kernel, translation invariant      234
Knot vector      134
Lattice, natural      200
Lattice, principal      201
Least interpolant      209
Leave-one-out technique      274
Locality      88
Loss, exponential      278
Loss, hinge      277
Loss, least-square      259 278
Lower set      223
Margin      277
Margin, maximal      277
Mask      63
Matrix coefficients      293 303
Matrix coefficients, orthogonality relations for      295
Matrix, central Hessian      177
Matrix, cross product      91
Matrix, discretized Gramian      91
Matrix, Fourier block      168
Matrix, G-equivalent      160
Matrix, influence      95
Matrix, observation      91
Matrix, subdivision      161
Matrix, unimodular      59
mesh      56
Mesh, refinement of      56
Moebius transformation      299
Multilevel method      246
Multiresolution analysis, intertwining      74
Nested iteration      93
Norm, $\varepsilon$ -insensitive      259
Normal equation      91
Normal form      216
Normal, central      154
Offset      278
Operator, analysis      292 293
Operator, Bernstein — Durrmeyer      3
Operator, Bernstein — Durrmeyer quasi-interpolant      10
Operator, dilation      318
Operator, Durrmeyer      3 284
Operator, projection      280
Operator, shape      181
Operator, subdivision      32
Operator, synthesis      292 293
Optimization, convex      268
Orthogonality relation      312
Outlier      97
Outlier, finding procedure      99
Parameterization      40
Parameterization, centripetal      41
Parameterization, chordal      41
Parameterization, Foley — Nielson      41
Parameterization, improvement      47
Parameterization, uniform      41
Partition of unity      243
Patch      152
Path of length n      205
Polygon, control      25
Polygon, control, edges of      25
Polygon, convex      28
Polygon, strictly convex      28
Polynomial, Bernstein basis      3 117
Polynomial, Jacobi      8
Polynomial, Lagrange fundamental      199
Polynomial, Laurent      59
Polynomial, leading coefficient of      207
Polynomial, Legendre      9
Polynomial, multidegree of      209
Polynomial, Newton fundamental      202
Polynomial, Newton fundamental, monomial      207
Polynomial, reduced      214
Polynomial, total degree of      199
Powell — Sabin 12-split      71
Prewavelet      61
Prewavelet, mask of      63
Proximity relation, 0-proximity      35
Proximity relation, 1-proximity      35
Pseudoaffinity      128
Quasi-interpolant, Bernstein — Durrmeyer      10
Reduction      215
Refinement equation      58
Refinement rule      25 27
Refitting criterion, global      99
Refitting criterion, local      101
Regression problem      258
Regression, logistic      278
Regularization      86
Regularization by smoothing      249
Regularization parameter      268
Regularization scheme      268
Regularization scheme, error decomposition      270
Regularization scheme, multi-kernel      284
Regularization term      86
Remainder of division      215
Representation      292
Representation, *-q-integrable      332

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