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Rice J.R. — The approximation of functions. Nonlinear and multivariate theory
Rice J.R. — The approximation of functions. Nonlinear and multivariate theory

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Название: The approximation of functions. Nonlinear and multivariate theory

Автор: Rice J.R.

Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1969

Количество страниц: 348

Добавлена в каталог: 19.11.2012

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$l_{1}$-norm      204
$L_{1}$-norm, weighted      288 289
$L_{2}$-approximation      226
$L_{2}$-approximation, by rationals      121
$L_{2}$-approximation, by splines      142
$L_{2}$-norm      225
$L_{p}$-approximation      298
$L_{p}$-approximation, $0 < p < 1$      288
$L_{p}$-approximation, existence theorems      48
$L_{p}$-approximation, norm      283 287
$L_{p}$-approximation, weighted      288 289
$L_{\infty}$-approximation      298
$M$-sphere      219
$n$-parameter families      1
$p$-tuple knot      131
$t$-density, noncentral      65
$\alpha$-convex      196
$\alpha$-Hull      196 222
$\gamma$-approximation problem      46
Ahlberg, J. H.      159
Alexander duality theorem      221
Algorithm, de la Vall$\acute{e}$e Poussin      13
Algorithm, exchange      122
Algorithm, Lawson      298
Algorithm, one-for-one exchange      254
Algorithm, perturbation, Remes      109
Algorithm, Polya      246
Algorithm, Remes      74 105 112
Algorithm, strict approximation      254
Alternation theorem      10
angle      177
Approximately compact      55
Approximating function, form      38
Approximating function, logarithmic      40
Approximating function, varisolvent      267
Approximation and interpolation      260
Approximation, $L_{p}$-      298
Approximation, $L_{t}$-      226
Approximation, $L_{\infty}$      298
Approximation, characterization, $L_{\infty}$      15 232
Approximation, existence      9
Approximation, existence theorems for $L_{p}$-      48
Approximation, finite point set      278
Approximation, linear functionals      154
Approximation, multivariate      224
Approximation, nonlinear      168
Approximation, nonlinear spline      129
Approximation, nonuniqueness      230
Approximation, problem      169
Approximation, pseudo      65
Approximation, stabilized      85 88
Approximation, strict      239 242 246
Approximation, Tchebycheff      56 298
Aro length      173
Ascent, method of      12 69
Assumption $\mathcal{A}$1      16
Assumption $\mathcal{A}$2      16 22
Atlas      171
Auslander, L.      171 184
Ball      173
Ball, unit      173
Banach space, strictly convex      173
Beckenbach, E. F.      153
Best approximation property      157
Betti number      222
Bing, R. H.      153
Birkhoff, G.      163 166
Boehm, B.      84 119
Boundedly compact      54
Brosowski, B.      77
Buck, R. C.      230 240
Buseman, H.      190
Caratheodory      94
cardinal splines      125 129
Carver, W. B.      120 234
Centers of curvature      211
Chains mod $\pi$      222
Characterization and existence      31
Characterizations of Tchebycheff approximations      15
Charts      171
Cheney, E. W.      40 77 90 101 102 113 116 120 121 235
Class 1 norm      265 280 304
Class 2 norm      265 280 304
Class 3 norm      280
Closed      16 34
Closed ball      173
Closer      293
Closure, parameter      82
Cody, W. T      104 111
Collatz, L.      237 259
Compaotifioation      219
Complex-valued functions      56
Computation      39 102 159 251 298
Condition E      80 118
Cone, support      180 181
Cone, tangent      175 181
Constraints, linear approximation problem with      170
Contact      192
Convex, uniformly      174
Coordinate neighborhoods      171 180
Critical point      92 202
Critical point, set      152 233 258
Critical point, strict      241
Critical point, with respect to $\mathcal{L}$      240
Curtis, A. R.      122
Curvature      190 192
Curvature, centers of      211
Curvature, radius of      192
Curve      191
Curve, of functions      46
Curves, equivalence classes of      184
Curves, smooth      123
Davis, P. J.      251
de la Vall$\acute{e}$e Poussin algorithm      13
deBoor, C.      143 158 159 161 163 166
Defect      97
Deformation retract      219
Degenerate      240
Degree      2 4 56 69
Degree, of varisolvence      59
Delta function      129
Dense nonzero property      84 118
Density, noncentral $t$-      65
Descloux, J.      246 248 254 256
Deviation vector      241
Differences, divided      126
Differentiable manifold      171
DIMENSION      181 240
Distance between two lines      177
Distance between two lines, maximal      206
Distributions      129
Distributions, uniform probability      127
Distributions, Weibul      40
Divided differences      126
Dot product      225
Double zero      4
Dual basis      158
Duality theorem, Alexander      221
Dugundji, J.      219
Dunham, C. B.      114 115
Efimof, N. V.      55 196 222
Eigenvalue problem      104
Equivalence classes of curves      184
Exactly interpolating function      261 289
Exchange algorithm      122
Exchange algorithm, for strict approximation      254
Existence and characterization      31
Existence and characterization, $L_{p}$-approximation      48
Existence and characterization, of best approximations      9
Exponential functions      40 42
Exponential functions, complex      40 62
Exponential rational functions      41
Extended spline      130
Extended totally positive      57 64
Extremal point      90 92 241
Fan, K.      90 93
Federer, H.      196 198 223
Fej$\acute{e}$r, L.      262 263
Fekete, M.      262
Fermi — Dirac integral      104 111
Finite point set, varisolvent approximations      278
Finite point set, varisolvent approximations, norm classes      279
Flat      173
Folding      210
Form of the approximating function      38
Formula, quadrature      126
Fraser, W.      104 110
Function, complex-valued      56
Function, delta      129
Function, exactly interpolating      261 289
Function, exponential      40 42
Function, exponential rational      41
Function, form of the approximating      38
Function, Gamma      103
Function, Green’s      158
Function, interpolating      260
Function, locally unisolvent      2 171
Function, logarithmic      40
Function, polynomial rational      97
Function, pseudo      66
Function, pseudo-rational      212
Function, rational      40 76
Function, representation of spline      159
Function, spline      183
Function, strongly interpolating      261 268
Function, trigonometric rational      40 101
Function, unisolvent      1 3 41
Function, varisolvent      2 56 65 214 267
Function, weakly interpolating      261 286 293
Functional, linear      154
Functional, representors      156
Functionals, approximation of linear      154
Functions, curve of      46
Fundamental spline      127
Gamma function      103
Gamma function, polynomial      46
General orthonormal systems      225
Generalized” splines      157 159
Geometric theory      168
Geometry, Minkowski      173
Girl’s profile      164
Global uniqueness theorem      207
Goffman, C.      33
Goldstein, A. A.      76 77 85 88 90 119 121 235
Golomb, M.      154 159
Gram — Schmidt process      251
Gram — Schmidt process, modified      252
Green’s function      158
Haar subspace      96
Haar subspace, theorem      230
Hart, J. F.      104 110
Height function      192
Hobby, C. R.      46
Holladay, J. C.      154
Hypercircle      154
Hyperplane      173
Hyperplane, support      173
Hyperplane, tangent      180
Inconsistent, irreducibly      93 118 234
Inequalities, system of linear      93 118
Inner product      225
Interpolating function      260
Interpolating function, on an interval      273
Interpolating function, strongly      261 288
Interpolating function, weakly      261 286 293
Interpolation      260
Interpolation, approximation and      260
Interpolation, problem, spline      160
Interpolation, property of splines      157
Irreducibly inconsistent      93 118 234
Isolable      233
Jackson, D.      269 272 273
Johnson, R. S.      153
Juxtapolynomial      293 304
Juxtapolynomial, on an interval      295
Karlin, S.      57 63 64 65 153 159
Kernel, reproducing      157 158
Knot      124
Knot, $p$-tuple      131
Lawson algorithm      298
Lawson, C. L.      259 262 298
Least-squares approximation      226
Lefschetz, S.      222
Limit sphere      174
Line      173
Line of support      180
Line, normal      189
Linear approximating function      226
Linear approximation problem with constraints      170
Linear functional      154
Linear inequalities      93 118
Linear method, weighted      119
Locally unisolvent      31
Locally unisolvent functions      2 171
Loeb, H. L.      40 77 101 102 113 116 117 120 121 122
Logarithmic approximating function      40
Lynch, R. E.      158 159 166
MacKensie, R. E.      171 184
Maehly second method      113
Maehly, H. J.      73 98 113
Mairhuber, J. C.      230
Manifold      171
Manifold, differentiable      84 118
Manifold, projections on a smooth      187
Manifold, unisolvent      172
Maximal distance      206
Meir, A.      163 167
Method of ascent      12 69 102
Metric      173
Minimal properties      157
Minkowski geometry      173
Minkowski geometry, space      173
Minus order      296
Minus order, zero      295
Modified Gram — Schmidt      252
Monospline      153
Monotonic norm      263 304
Motzkin, T. S.      1 168 198 262 269 273 277 280 295 304 305
Multivariate approximation      224
Natural splines      129
Negative points      233
Neighborhoods, coordinate      180
Newman, D. J.      259
Newton’s method      105
Nilson, E. N.      159
Non-manifold problems      212
Noncentral $t$-density      65
Nonlinear approximations      168
Nonlinear approximations, spline approximation      129 161
Norm      225 260 263
Norm, $L_{1}$-      204
Norm, $L_{2}$-      225
Norm, $L_{p}$-      283 287
Norm, class 1      265 280 304
Norm, class 2      265 280 304
Norm, class 3      280
Norm, classes      265
Norm, classes for finite point sets      279
Norm, monotonic      263 304
Norm, strict      174
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