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| Авторизация |
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| Rice J.R. — The approximation of functions. Nonlinear and multivariate theory |
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| Предметный указатель |
Norm, Tchebycheff 3 290
Norm, weighted  - 288 289
Norm, weighted  - 288 289
Norm, weighted Tchebycheff 290
normal 101 189
Normal, equations 228
Normal, line 189
Normal, ray 189
Normal, set 189
Nup point 197 211
Nup(F) 219
One-for-one exchange algorithm 254
Order, minus 296
Order, plus 296
Orthogonal 225
Orthogonal system 226
Orthonormal spline 142
Orthonormal spline, systems, general 225
Parameter closure 82
Parameter closure, space, topology 5
Peano’s theorem 126
Periodic splines 166
Perpendicular 174
Perturbation, Remes algorithm 109
Piecewise polynomials 123
Pivoting 253
Plane of support 174
Plane of support, tangent 174 184 185
Plus, order 296
Plus, order, zero 295
Point, critical 192 202
Point, extremal 90 92 241
Point, nup 197 211
Point, positive and negative 233
Polya Algorithm 246
Polynomials, piecewise 123
Polynomials, rationals 97
Popoviciu 153
Positive and negative points 233
Poussin, de la Vall e, algorithm 13
Powell, M. J. D. 122
Probability distribution, uniform 127
Product space 227
Product space, tensor 227
Projection 169 176
Projection, on a smooth manifold 187
Projection, on objects 217
Projection, on submanifolds 201
Projection, operator 156 170
Projection, problem 168 169
Projection, property, unique 198
Projection, unique 176 197 209
Property A 2 17
Property N 15
Property NS 15 18 24 34
Property S 15 18
Property Z 2 3 18 24 39
Pseudo-approximation 65
Pseudo-approximation, function 66
Pseudo-approximation, rational functions 212 4
Quadrature formula 126
Rabinowitz, P. 251
Radius of curvature 192
Ralston, A. 110
RANGE 22
Rational functions 40 76
Rational functions, exponential 41
Rational functions, polynomial 97
Rational functions, pseudo 212
Rational functions, trigonometric 40 101
Ray 173
Ray, normal 189
Reach 196 197 218
Regularity 263
Remes algorithm 74 105 112
Remes algorithm—perturbation 109
Remes, E. 239
Representation of spline function 159
Representers, functional 156
Reproducing kernel 157 168
Retract, deformation 219
Rice, J. R. 1 2 6 15 39 41 46 151 161 163 190 203 209 233 239 254 262 278 280 298 304 305
Rivlin, T. J. 120 235 238
Sard A. 154
Schoenberg, I. J. 123 127 153 159 166
Schumaker, L. 153
Segment 173
Sequences of varisolvent functions 6
Set, critical point 152 233 258
Set, Motzkin 198 223
Set, norm classes 279
Set, normal 189
Set, smooth 183
Set, Tchebycheff 56 61 96 168 231 284
Set, tripod-like 230
Shapiro, H. S. 235 238 259
Sharma, A. 163 167
Sign change 261
Smooth 174 198
Smooth curves 123
Smooth set 183
Solvence 3 24 39
Southard, T. H. 113
Space, Minkowski 173
Space, product 227
| Space, tangent 180 184
Sphere,  - 210
Sphere, limit 174
Sphere, support 196
Sphere, unit 174
Spline approximation 123
Spline approximation, cardinal 125 129
Spline approximation, extended 130
Spline approximation, function 46 123
Spline approximation, function, representation of 159
Spline approximation, fundamental 127
Spline approximation, interpolation problem 160
Spline approximation, interpolation property 157
Spline approximation, natural 129
Spline approximation, nonlinear 129 161
Spline approximation, orthonormal 142
Spline approximation, periodic 166
Spline approximation, trigonometric 171
Spline approximation, “generalized” 157 159
Stabilized best approximations 85 88
Steckin, S. B. 55 196 222
Stiefel, E. L. 258
Stoer, J. 110
Stone, H. 164
Strict approximation 239 242 246
Strict critical point set 241
Strictly convex Banach space 173
Strictly convex Banach space, normed 174
Strictly convex Banach space, totally positive 64
Strong sign changes 261
Strong sign changes, uniqueness theorem 95
Strongly interpolating function 261 288
Studden, W. J. 159
Submanifolds of  180
Subset theorem 12
Subspace, Haar 96
Support cone 180 181
Support cone, hyperplane 173
Support cone, line 180
Support cone, plane 174
Support cone, sphere 196
System of linear inequalities 93 118
Szego, G. 127 167
Tangent cone 175 171
Tangent hyperplane 180
Tangent plane 174 184 185
Tangent space 180 184
Taylor’s series with exact remainder 125
Tchebycheff approximation 56 298
Tchebycheff approximation by splines 145
Tchebycheff approximation—characterization 10 15 31 56 232
Tchebycheff approximation—nonuniqueness 230
Tchebycheff norm 3 290
Tchebycheff set 56 61 96 168 231 284
Tchebycheff set, several variables 230
Tchebycheff-type theory 2 15
Tensor products 227
Thacher, H. C. 104 111
Theorem of de la Valle Poussin 12
Topology of parameter space 5 212
Tornheim, L. 1 153
Totally positive 57
Totally positive, strictly 64
Transversal 174
triangle 177
Trigonometric rational functions 40 101
Trigonometric rational functions, spline 171
Tripod-like set 230
Uniform probability distributions 127
Uniformly convex 174
Unique projection 176 197 209
Unique projection, property 198
Uniqueness theorem, global 207
Uniqueness theorem, of varisolvent approximations 12
Uniqueness theorem, strong 95
Unisolvent, functions 1 3 41 172 204
Unisolvent, functions, locally 2 31 171
Unisolvent, manifolds 172
Unit ball 173
Unit ball, sphere 174
Unsolved problems 38
Usow, K. H. 298 304
Variational lemma 235
Varisolvence 24 267
Varisolvence, degree of 59
Varisolvent approximating function 1 56 65 97 214 267
Varisolvent approximating function, approximations, finite point set 278
Varisolvent approximating function, approximation—uniqueness 12
Varisolvent approximating function, functions, sequences 6
Von Neuman, J. 262
Walsh, J. L. 159 163 262 269 273 277 280 295 304 305
Weak sign changes 260
Weakly interpolating function 261 286 293
Weibul distribution 40
Weighted -norm 288 289
Weighted -norm, linear method 119
Weighted -norm, Tchebycheff norm 290
Weinberger, H. F. 154 159
Werner, H. 101 105 110
Whitney, Anne 127
Witzgall, Ch 98
Zero 4 261
Zero, double 4
Zero, minus 295
Zero, order 2 295
Zero, plus 295
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