Ahlberg J.H., Nilson E.N., WAlsh J.L. — The Theory of Splines and Their Applications :: Электронная библиотека попечительского совета мехмата МГУ

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

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Название: The Theory of Splines and Their Applications

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

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1967

Количество страниц: 284

Добавлена в каталог: 14.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный 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 “Cubic spline”
Bellman, R.E.      56
Best approximation property      4
Best approximation property for cubic splines      16—19 77—78
Best approximation property for doubly cubic splines      244—245
Best approximation property for generalized uplines      200—201
Best approximation property for polynomial splines      157—159
Bicubic splines      5—6 (see also “Doubly cubic splines”)
Birkhoff, G.      4 5 29 237
Birkhoff, G., definition of      275
Canonical mesh bases for cubic splines      101—103
Canonical mesh bases for doubly cubic splines      249
Canonical mesh bases for generalized splines      219—220 275
Canonical mesh bases for polynomial splines      179—182
Cardmal splines      52—53 245—247 251—254
Circulant matrix      36 133 148—149
Convergence in norm for cubic splines      98—101
Convergence in norm for doubly cubic splines      247—248
Convergence in norm for generalized splines      214—219
Convergence in norm for polynomial splines      176—179
Convergence properties      4—5
Convergence properties for cubic splines      19—34 61—74 87—96
Convergence properties for doubly cubic splines      247—248
Convergence properties for generalized splines      201—212 274
Convergence properties for polynomial splines      135—143 148—152 166—174
Coons surfaces      262—264
Cubic splines 1      9—108
Cubic splines 1, best approximation property      16—19 77—78
Cubic splines 1, canonical mesh bases      101—103
Cubic splines 1, cardinal splines      52—58
Cubic splines 1, convergence      19—34 61—74 87—96
Cubic splines 1, convergence m norm      93—101
Cubic splines 1, curve fitting      50—52
Cubic splines 1, deficiency of      24
Cubic splines 1, defining values      82 97
Cubic splines 1, end conditions      11 13—14 50
Cubic splines 1, equal intervals      9 34—42
Cubic splines 1, equations for      10—16 84—87
Cubic splines 1, existence      16—19 61—74 84
Cubic splines 1, first integral relation      77—82
Cubic splines 1, fundamental identity      78—79
Cubic splines 1, Hilbert space theory of      97—107
Cubic splines 1, integral equations      57—59
Cubic splines 1, linear functionals      103—107
Cubic splines 1, minimum norm property      75—77
Cubic splines 1, orthogonality      97—101
Cubic splines 1, parametric splines      51
Cubic splines 1, periodic cubjc splines      10
Cubic splines 1, second integral relation      89—91
Cubic splines 1, simple cubic splines      78
Cubic splines 1, spline-on-a-spline      44 48—50
Cubic splines 1, type I      75
Cubic splines 1, type I'      75
Cubic splines 1, type II      75
Cubic splines 1, type II’      75
Cubic splines 1, uniqueness      16—19 82—83
Cumulative chord length      51 254—262
Curve fitting      1—2 50—52 143
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      191—192
Deficiency of a spline for polynomial splines      123 143—147 157 163—164
Deficiency of a spline for quintic splines      123 143—148
Defining values      82 97 175 235
Degree of a spline      109
Differential equations      52—57 228—233
Differentiation      see “Numerical differentiation”
Direct products (of Hubert spaces)      249
Doubly cubic splines      5 235—264
Doubly cubic splines, $\mathcal{K}_m^n(\mathcal{R})$       275
Doubly cubic splines, best approximation property      244—245
Doubly cubic splines, canonical mesh bases      249
Doubly cubic splines, cardinal splines      245—247 251—254
Doubly cubic splines, convergence      247—248
Doubly cubic splines, convergence in norm      250
Doubly cubic splines, defining values      235
Doubly cubic splines, doubly periodic splines      236
Doubly cubic splines, existence      239 243—244
Doubly cubic splines, first integral relation      242
Doubly cubic splines, fundamental identity      240—242
Doubly cubic splines, Hilbeit space theory      249—251
Doubly cubic splines, irregular regions      254—258
Doubly cubic splines, minimum norm property      242—243
Doubly cubic splines, partial differential equations      251—254
Doubly cubic splines, partial splines      237—239
Doubly cubic splines, second integral relation      248
Doubly cubic splines, simple doubly cubic splines      235
Doubly cubic splines, surfaces      256—262
Doubly cubic splines, type I      235—236
Doubly cubic splines, type I'      236
Doubly cubic splines, type II      236
Doubly cubic splines, type II'      236
Doubly cubic splines, uniqueness      239 243—244
Doubly periodic splines      236
Eigenvalue problem      57—58 228—230
Elastica      1 3
End conditions, cubic splines      11 13—14 50
End conditions, curve fitting      50
End conditions, modified type k      170
End conditions, polynomial splines      122—123 158
End conditions, type I      75 113 193—194 235—236
End conditions, type I'      75 113 193—194 236
End conditions, type II      75 313 193—194 236
End conditions, type II'      75 113 193—194 236
End conditions, type k      167—168 194
Equal intervals, cubic splines      9 34—42
Equal intervals, polynomial splines      124—135 148—152
Existence of splines      2
Existence of splines, of cubic splines      16—19 61—74 84
Existence of splines, of doubly cubic splines      239 243—244
Existence of splines, of generalized splines      199—200 272—274
Existence of splines, of polynomial splines      132—335 165—866
Explicit type      269—270
Fejer, L.      23—24 147—148
First integral relation      3
First integral relation for cubic splines      77—82
First integral relation for doubly cubic splines      242
First integral relation for generalized sphnes      193—195 270 271
First integral relation for polynomial sphnes      155—156
Fundamental identity      392—193 267—269
Fundamental identiy for cubic splines      78—79
Fundamental identiy for doubly cubic splines      240—242
Fundamental identiy for generalized splines      192—193 267—269
Fundamental identiy for polynomial splines      154—155
Garabedian, H.      5 237
Generalized splines      6 191—233 265—276
Generalized splines, best approximation property      200—201
Generalized splines, canonical mesh bases      239—220 275
Generalized splines, convergence      203—212 274
Generalized splines, convergence in norm      234—239
Generalized splines, deficiency of      191—192
Generalized splines, differential equations      228—233
Generalized splines, equations for      197—399
Generalized splines, existence      199—200 272—274
Generalized splines, explicit type      269—270
Generalized splines, first integral relation      393—195 270—271

Generalized splines, Hilbert space theory      213—233 275—276
Generalized splines, integral equations      230—232
Generalized splines, linear functional      220—233 275—276
Generalized splines, minimum norm property      195—196 271—272
Generalized splines, numerical integration      224—228
Generalized splines, order of      393
Generalized splines, orthogonality      238
Generalized splines, partial differential equations      276
Generalized splines, partial splines      273
Generalized splines, Peano kernels      220—224
Generalized splines, periodic splines      194
Generalized splines, second integral relation      204—206
Generalized splines, simple splines      194
Generalized splines, strong interpolation      270
Generalized splines, two-dimensional      265—276
Generalized splines, type I      193—194
Generalized splines, type I'      193—194
Generalized splines, type II      193—194
Generalized splines, type II'      193—194
Generalized splines, type k      394
Generalized splines, uniqueness      196—197 271—272
Generalized splines, uniqueness property      272
Gershgorm’s theorem      16
Golomb, M.      7—8
Greville, T.N.E.      4 6 105
heterogeneous splines      394
Hilbert space theory      3—4
Hilbert space theory for cubic splines      97—107
Hilbert space theory for doubly cubic splines      249—251
Hilbert space theory for generalized splines      213—233 275—276
Hilbert space theory for polynomial splines      174—190
Hille, E      134
Holladay, J.C.      3 8 46 75 77 73 80
Integral equations      57—61 230—232
Integration      see “Numerical integration”
Irregular regions      254—258
Kalaba, R.E.      56
Limits on convergence      95—96 174 211—212
Linear functional      6—7 103—107 185—189 220—233 275—276
Lynch, R.E.      4 6 7
Mathematical spline      1 9
Meir, A      4 27
Mesh bases      101—103 179—182
Mesh restrictions      22 25 94—95
Method of cardinal splines      see “Cardinal splines”
Minimum curvature property      2 3
Minimum norm property      3
Minimum norm property for cubic splines      75—77
Minimum norm property for doubly cubic splines      242—243
Minimum norm property for generalized splines      195—196 271—272
Minimum norm property for polynomial splines      156—157
Modified type k      170 (see also “Type k”)
Multidimensional splines      5 6
Nilson, E.N.      2 3 5 7 70 78 136 140 142 237
Nonlinear differential equations      56
Numerical differentiation      42—57
Numerical integration      42—50 145—146 224—228
Order of a spline      191
Orthogonality, cubic splines      97—101
Orthogonality, generalized splines      213—219
Orthogonality, polynomial splines      174—179 (see also “Canonical mesh bases”)
Parametric splines      51 254—258
Parametric splines, surfaces      258—262
Partial differential equations, numerical solution of      251—254 276
Partial splines      237—239 273
Peano kernel      6 103—105 182—189 220—224
Peano, G      105 185
Periodic splines      10 148—152 156 167 194 236
Polynomial splines      109—189
Polynomial splines, best approximation property      157—159
Polynomial splines, canonical mesh bases      179—182
Polynomial splines, convergence      135—143 148—152 166—174
Polynomial splines, convergence m norm      176—179
Polynomial splines, deficiency of      123 143—148 157 163—164
Polynomial splines, defining values      175
Polynomial splines, degree of      109
Polynomial splines, end conditions      122—123 158
Polynomial splines, equal intervals      124—135 148—152
Polynomial splines, equations for      109—123 160—165
Polynomial splines, even degree      109—110 153
Polynomial splines, existence of      132—135 165—166
Polynomial splines, first integral relation      155—156
Polynomial splines, fundamental identity      154—155
Polynomial splines, Hilbert space theory      174—189
Polynomial splines, limits on convergence      174
Polynomial splines, linear functional      185—189
Polynomial splines, minimum norm property      156—157
Polynomial splines, modified type k      170
Polynomial splines, numerical integration      145—146
Polynomial splines, odd degree      5 153—189
Polynomial splines, orthogonality      174—179
Polynomial splines, Peano kernels      182—189
Polynomial splines, periodic splines      148—152 156 167
Polynomial splines, quintic splines      143—148
Polynomial splines, remainder formulas      185—139
Polynomial splines, second integral relation      168—170
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      167—168
Polynomial splines, uniform mesh      148—152
Polynomial splines, uniqueness      159—160
Qmntic splines      143—148
Quadrature      see “Numerical integration”
Remainder formulas      303—105 185—189 221—228
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      89—91
Second integral relation for double cubic splines      248
Second integral relation for generalised splines      204—206
Second integral relation for polynomial splines      168—170
Secrest, D.      8
Sharma, A.      4 27
Simple splines      7 78 113 194 235
Sokolnikoff, I.S.      2 3 77
Space technology      107—108
Spline equations for cubic splines      10—16 84—87
Spline equations for generalized splines      197—199
Spline equations for polynomial splines      109—123 160—165
Spline surfaces      256—262 (see also “Coons surfaces”)
Spline-on-spline      44 48—50
Splines in tension      6
Splines of even degree      109—110 153
Splines of odd degree      153—389 (see also “Polynomial splines cubic
Strong interpolation      270
Surfaces      see “Spline surfaces” “Coons
Two-dimensional splines, doubly cubic splines      235—264
Two-dimensional splines, generalized splines      265—276
Type I      75 113 193—194 235—236
Type I'      75 113 193—154 236
Type II      75 113 193—194 236
Type II'      75 113 193—194 236
Type k      167—168 170 194
Uniform mesh      148—152 (see also “Equal intervals”)
Uniqueness of cubic splines      16—19 82—83
Uniqueness of doubly cubic splines      239 243—244
Uniqueness of generalized splines      196—197 271—272
Uniqueness of polynomial splines      159—160
Uniqueness property      272
Walsh; J.L.      2 3 4 5 6 7 78 136 140 142 237
Weinberger, H.F.      7—8
Whitney, A.      2
Ziegler, Z.      5 136

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