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Ahlberg J.H., Nilson E.N., WAlsh J.L. Ч The Theory of Splines and Their Applications
Ahlberg J.H., Nilson E.N., WAlsh J.L. Ч The Theory of Splines and Their Applications



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Ќазвание: The Theory of Splines and Their Applications

јвторы: Ahlberg J.H., Nilson E.N., WAlsh J.L.

язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1967

 оличество страниц: 284

ƒобавлена в каталог: 14.05.2008

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
$\mathcal{K}^n(a,b)$, definition of      75
$\mathcal{K}^n_m(\mathcal{R})$, definition of      275
$\mathcal{K}^n_P(a,b)$, definition of      75
Ahlberg, J.R.      2 3 4 5 6 7 70 78 136 140 142 237
Atteia, M.      6
Auslender, S.      143
Beam theory      1 3 77
Beamfit      see УCubic splineФ
Bellman, R.E.      56
Best approximation property      4
Best approximation property for cubic splines      16Ч19 77Ч78
Best approximation property for doubly cubic splines      244Ч245
Best approximation property for generalized uplines      200Ч201
Best approximation property for polynomial splines      157Ч159
Bicubic splines      5Ч6 (see also УDoubly cubic splinesФ)
Birkhoff, G.      4 5 29 237
Birkhoff, G., definition of      275
Canonical mesh bases for cubic splines      101Ч103
Canonical mesh bases for doubly cubic splines      249
Canonical mesh bases for generalized splines      219Ч220 275
Canonical mesh bases for polynomial splines      179Ч182
Cardmal splines      52Ч53 245Ч247 251Ч254
Circulant matrix      36 133 148Ч149
Convergence in norm for cubic splines      98Ч101
Convergence in norm for doubly cubic splines      247Ч248
Convergence in norm for generalized splines      214Ч219
Convergence in norm for polynomial splines      176Ч179
Convergence properties      4Ч5
Convergence properties for cubic splines      19Ч34 61Ч74 87Ч96
Convergence properties for doubly cubic splines      247Ч248
Convergence properties for generalized splines      201Ч212 274
Convergence properties for polynomial splines      135Ч143 148Ч152 166Ч174
Coons surfaces      262Ч264
Cubic splines 1      9Ч108
Cubic splines 1, best approximation property      16Ч19 77Ч78
Cubic splines 1, canonical mesh bases      101Ч103
Cubic splines 1, cardinal splines      52Ч58
Cubic splines 1, convergence      19Ч34 61Ч74 87Ч96
Cubic splines 1, convergence m norm      93Ч101
Cubic splines 1, curve fitting      50Ч52
Cubic splines 1, deficiency of      24
Cubic splines 1, defining values      82 97
Cubic splines 1, end conditions      11 13Ч14 50
Cubic splines 1, equal intervals      9 34Ч42
Cubic splines 1, equations for      10Ч16 84Ч87
Cubic splines 1, existence      16Ч19 61Ч74 84
Cubic splines 1, first integral relation      77Ч82
Cubic splines 1, fundamental identity      78Ч79
Cubic splines 1, Hilbert space theory of      97Ч107
Cubic splines 1, integral equations      57Ч59
Cubic splines 1, linear functionals      103Ч107
Cubic splines 1, minimum norm property      75Ч77
Cubic splines 1, orthogonality      97Ч101
Cubic splines 1, parametric splines      51
Cubic splines 1, periodic cubjc splines      10
Cubic splines 1, second integral relation      89Ч91
Cubic splines 1, simple cubic splines      78
Cubic splines 1, spline-on-a-spline      44 48Ч50
Cubic splines 1, type I      75
Cubic splines 1, type I'      75
Cubic splines 1, type II      75
Cubic splines 1, type IIТ      75
Cubic splines 1, uniqueness      16Ч19 82Ч83
Cumulative chord length      51 254Ч262
Curve fitting      1Ч2 50Ч52 143
Dahlqulst, G.      233
Davis, P.J.      19 220
de Eoor, C.      4 5 6 7 29 237
Deficiency of a spline      7
Deficiency of a spline for cubic splines      24
Deficiency of a spline for generalized splines      191Ч192
Deficiency of a spline for polynomial splines      123 143Ч147 157 163Ч164
Deficiency of a spline for quintic splines      123 143Ч148
Defining values      82 97 175 235
Degree of a spline      109
Differential equations      52Ч57 228Ч233
Differentiation      see УNumerical differentiationФ
Direct products (of Hubert spaces)      249
Doubly cubic splines      5 235Ч264
Doubly cubic splines, $\mathcal{K}_m^n(\mathcal{R})$      275
Doubly cubic splines, best approximation property      244Ч245
Doubly cubic splines, canonical mesh bases      249
Doubly cubic splines, cardinal splines      245Ч247 251Ч254
Doubly cubic splines, convergence      247Ч248
Doubly cubic splines, convergence in norm      250
Doubly cubic splines, defining values      235
Doubly cubic splines, doubly periodic splines      236
Doubly cubic splines, existence      239 243Ч244
Doubly cubic splines, first integral relation      242
Doubly cubic splines, fundamental identity      240Ч242
Doubly cubic splines, Hilbeit space theory      249Ч251
Doubly cubic splines, irregular regions      254Ч258
Doubly cubic splines, minimum norm property      242Ч243
Doubly cubic splines, partial differential equations      251Ч254
Doubly cubic splines, partial splines      237Ч239
Doubly cubic splines, second integral relation      248
Doubly cubic splines, simple doubly cubic splines      235
Doubly cubic splines, surfaces      256Ч262
Doubly cubic splines, type I      235Ч236
Doubly cubic splines, type I'      236
Doubly cubic splines, type II      236
Doubly cubic splines, type II'      236
Doubly cubic splines, uniqueness      239 243Ч244
Doubly periodic splines      236
Eigenvalue problem      57Ч58 228Ч230
Elastica      1 3
End conditions, cubic splines      11 13Ч14 50
End conditions, curve fitting      50
End conditions, modified type k      170
End conditions, polynomial splines      122Ч123 158
End conditions, type I      75 113 193Ч194 235Ч236
End conditions, type I'      75 113 193Ч194 236
End conditions, type II      75 313 193Ч194 236
End conditions, type II'      75 113 193Ч194 236
End conditions, type k      167Ч168 194
Equal intervals, cubic splines      9 34Ч42
Equal intervals, polynomial splines      124Ч135 148Ч152
Existence of splines      2
Existence of splines, of cubic splines      16Ч19 61Ч74 84
Existence of splines, of doubly cubic splines      239 243Ч244
Existence of splines, of generalized splines      199Ч200 272Ч274
Existence of splines, of polynomial splines      132Ч335 165Ч866
Explicit type      269Ч270
Fejer, L.      23Ч24 147Ч148
First integral relation      3
First integral relation for cubic splines      77Ч82
First integral relation for doubly cubic splines      242
First integral relation for generalized sphnes      193Ч195 270 271
First integral relation for polynomial sphnes      155Ч156
Fundamental identity      392Ч193 267Ч269
Fundamental identiy for cubic splines      78Ч79
Fundamental identiy for doubly cubic splines      240Ч242
Fundamental identiy for generalized splines      192Ч193 267Ч269
Fundamental identiy for polynomial splines      154Ч155
Garabedian, H.      5 237
Generalized splines      6 191Ч233 265Ч276
Generalized splines, best approximation property      200Ч201
Generalized splines, canonical mesh bases      239Ч220 275
Generalized splines, convergence      203Ч212 274
Generalized splines, convergence in norm      234Ч239
Generalized splines, deficiency of      191Ч192
Generalized splines, differential equations      228Ч233
Generalized splines, equations for      197Ч399
Generalized splines, existence      199Ч200 272Ч274
Generalized splines, explicit type      269Ч270
Generalized splines, first integral relation      393Ч195 270Ч271
Generalized splines, Hilbert space theory      213Ч233 275Ч276
Generalized splines, integral equations      230Ч232
Generalized splines, linear functional      220Ч233 275Ч276
Generalized splines, minimum norm property      195Ч196 271Ч272
Generalized splines, numerical integration      224Ч228
Generalized splines, order of      393
Generalized splines, orthogonality      238
Generalized splines, partial differential equations      276
Generalized splines, partial splines      273
Generalized splines, Peano kernels      220Ч224
Generalized splines, periodic splines      194
Generalized splines, second integral relation      204Ч206
Generalized splines, simple splines      194
Generalized splines, strong interpolation      270
Generalized splines, two-dimensional      265Ч276
Generalized splines, type I      193Ч194
Generalized splines, type I'      193Ч194
Generalized splines, type II      193Ч194
Generalized splines, type II'      193Ч194
Generalized splines, type k      394
Generalized splines, uniqueness      196Ч197 271Ч272
Generalized splines, uniqueness property      272
GershgormТs theorem      16
Golomb, M.      7Ч8
Greville, T.N.E.      4 6 105
heterogeneous splines      394
Hilbert space theory      3Ч4
Hilbert space theory for cubic splines      97Ч107
Hilbert space theory for doubly cubic splines      249Ч251
Hilbert space theory for generalized splines      213Ч233 275Ч276
Hilbert space theory for polynomial splines      174Ч190
Hille, E      134
Holladay, J.C.      3 8 46 75 77 73 80
Integral equations      57Ч61 230Ч232
Integration      see УNumerical integrationФ
Irregular regions      254Ч258
Kalaba, R.E.      56
Limits on convergence      95Ч96 174 211Ч212
Linear functional      6Ч7 103Ч107 185Ч189 220Ч233 275Ч276
Lynch, R.E.      4 6 7
Mathematical spline      1 9
Meir, A      4 27
Mesh bases      101Ч103 179Ч182
Mesh restrictions      22 25 94Ч95
Method of cardinal splines      see УCardinal splinesФ
Minimum curvature property      2 3
Minimum norm property      3
Minimum norm property for cubic splines      75Ч77
Minimum norm property for doubly cubic splines      242Ч243
Minimum norm property for generalized splines      195Ч196 271Ч272
Minimum norm property for polynomial splines      156Ч157
Modified type k      170 (see also УType kФ)
Multidimensional splines      5 6
Nilson, E.N.      2 3 5 7 70 78 136 140 142 237
Nonlinear differential equations      56
Numerical differentiation      42Ч57
Numerical integration      42Ч50 145Ч146 224Ч228
Order of a spline      191
Orthogonality, cubic splines      97Ч101
Orthogonality, generalized splines      213Ч219
Orthogonality, polynomial splines      174Ч179 (see also УCanonical mesh basesФ)
Parametric splines      51 254Ч258
Parametric splines, surfaces      258Ч262
Partial differential equations, numerical solution of      251Ч254 276
Partial splines      237Ч239 273
Peano kernel      6 103Ч105 182Ч189 220Ч224
Peano, G      105 185
Periodic splines      10 148Ч152 156 167 194 236
Polynomial splines      109Ч189
Polynomial splines, best approximation property      157Ч159
Polynomial splines, canonical mesh bases      179Ч182
Polynomial splines, convergence      135Ч143 148Ч152 166Ч174
Polynomial splines, convergence m norm      176Ч179
Polynomial splines, deficiency of      123 143Ч148 157 163Ч164
Polynomial splines, defining values      175
Polynomial splines, degree of      109
Polynomial splines, end conditions      122Ч123 158
Polynomial splines, equal intervals      124Ч135 148Ч152
Polynomial splines, equations for      109Ч123 160Ч165
Polynomial splines, even degree      109Ч110 153
Polynomial splines, existence of      132Ч135 165Ч166
Polynomial splines, first integral relation      155Ч156
Polynomial splines, fundamental identity      154Ч155
Polynomial splines, Hilbert space theory      174Ч189
Polynomial splines, limits on convergence      174
Polynomial splines, linear functional      185Ч189
Polynomial splines, minimum norm property      156Ч157
Polynomial splines, modified type k      170
Polynomial splines, numerical integration      145Ч146
Polynomial splines, odd degree      5 153Ч189
Polynomial splines, orthogonality      174Ч179
Polynomial splines, Peano kernels      182Ч189
Polynomial splines, periodic splines      148Ч152 156 167
Polynomial splines, quintic splines      143Ч148
Polynomial splines, remainder formulas      185Ч139
Polynomial splines, second integral relation      168Ч170
Polynomial splines, simple splines      113
Polynomial splines, type I      113
Polynomial splines, type I'      113
Polynomial splines, type II      113
Polynomial splines, type II'      113
Polynomial splines, type k      167Ч168
Polynomial splines, uniform mesh      148Ч152
Polynomial splines, uniqueness      159Ч160
Qmntic splines      143Ч148
Quadrature      see УNumerical integrationФ
Remainder formulas      303Ч105 185Ч189 221Ч228
Sard, A.      6 105 185 222 227 233 275
Schoenberg, I.J.      2 4 5 6 7 44 75 106 185
Schweikert, D.G.      6
Second integral relation      5
Second integral relation for cubic splines      89Ч91
Second integral relation for double cubic splines      248
Second integral relation for generalised splines      204Ч206
Second integral relation for polynomial splines      168Ч170
Secrest, D.      8
Sharma, A.      4 27
Simple splines      7 78 113 194 235
Sokolnikoff, I.S.      2 3 77
Space technology      107Ч108
Spline equations for cubic splines      10Ч16 84Ч87
Spline equations for generalized splines      197Ч199
Spline equations for polynomial splines      109Ч123 160Ч165
Spline surfaces      256Ч262 (see also УCoons surfacesФ)
Spline-on-spline      44 48Ч50
Splines in tension      6
Splines of even degree      109Ч110 153
Splines of odd degree      153Ч389 (see also УPolynomial splines cubic
Strong interpolation      270
Surfaces      see УSpline surfacesФ УCoons
Two-dimensional splines, doubly cubic splines      235Ч264
Two-dimensional splines, generalized splines      265Ч276
Type I      75 113 193Ч194 235Ч236
Type I'      75 113 193Ч154 236
Type II      75 113 193Ч194 236
Type II'      75 113 193Ч194 236
Type k      167Ч168 170 194
Uniform mesh      148Ч152 (see also УEqual intervalsФ)
Uniqueness of cubic splines      16Ч19 82Ч83
Uniqueness of doubly cubic splines      239 243Ч244
Uniqueness of generalized splines      196Ч197 271Ч272
Uniqueness of polynomial splines      159Ч160
Uniqueness property      272
Walsh; J.L.      2 3 4 5 6 7 78 136 140 142 237
Weinberger, H.F.      7Ч8
Whitney, A.      2
Ziegler, Z.      5 136
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