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Arcangeli R. — Multidimensional Minimizing Splines
Arcangeli R. — Multidimensional Minimizing Splines



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Название: Multidimensional Minimizing Splines

Автор: Arcangeli R.

Аннотация:

This book is meant for mathematicians, geologists, engineers and, in general, researchers and postgraduate students involved in spline function theory, surface fitting problems or variational methods.


Язык: en

Рубрика: Технология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 261

Добавлена в каталог: 09.07.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$D^m$-spline, basis $D^m$-splines      64
$D^m$-spline, over $\mathbb{R}^{n}$      ix 3
$D^m$-spline, over $\Omega \setminus \bar{F}$      136—140
$D^m$-spline, over $\Omega$      ix 59 “Smoothing over
$D^m$-spline, over $\Omega$, regularity      65
$D^m$-spline, space of s over O      64
$D^m$-spline, univariate $D^m$-spline      see “Univariate $D^m$-spline”
$P_{l}$-unisolvent set      xv
$V_h$-discrete interpolating $D^m$-spline      see “Discrete interpolating $D^m$-spline”
$V_h$-discrete smoothing $D^m$-spline      see “Discrete smoothing $D^m$-spline”
$X_h$-discrete smoothing $D^m$-spline      see “Discrete smoothing $D^m$-spline”
$X_h$-discrete smoothing $D^m$-spline with tangent conditions      225
(m,l,s)-spline      see “Interpolating” and “Smoothing (m
(m,s)-spline      ix 3
(m,s)-spline, explicit expression      17
(m,s)-spline, regularity      20
(m,s)-spline, space of (m,s)-splines      15
Adams, R.A.      xiv 50 136 201
Akima, H.      132
Allasia, G.      132 160
Andor, L.      227
Apprato, D.      61 80 87 100 105 107 175 199 222
Approximation error of discrete, interpolating $D^m$-splines      80
Approximation error of discrete, smoothing $D^m$-splines      87
Approximation error of interpolating, $D^m$-splines over $\Omega$      68
Approximation error of interpolating, (m,l,s)-splines      55
Approximation error of interpolating, (m,s)-splines      37
Approximation error of smoothing, $D^m$-splines over $\Omega$      68
Approximation error of smoothing, (m,l,s)-splines      56
Approximation error of smoothing, (m,s)-splines      49
Approximation operator      70
Arcangeli, R.      32 33 45 47—49 52 61 75 87 105 107 131 132 147 175 199 222
Arge, E.      132
Argyris triangle      71 108
Argyris triangle, of class $C^1$      107 109
Argyris triangle, of class $C^2$      107—110
Aronszajn, N.      3
Arsenine, V.      81
Atteia, M.      ix 3 59
B-spline      ix 98
Banach — Steinhaus theorem      34
Banach's isomorphism theorem      9 11
Basis $D^m$-splines      64
Basis of normalized cubic B-splines      98
Bell triangle      71 108
Bell triangle, of class $C^1$      107—109
Bell triangle, of class $C^2$      107—110
Benbourhim, M.N.      24
Bernardi, C.      145
Besenghi, R.      132 160
Bezier surface      ix
Bogner — Fox — Schmit rectangle      71 108
Bogner — Fox — Schmit rectangle of class $C^1$      88
Bogner — Fox — Schmit rectangle, of class $C^1$      107 109
Bogner — Fox — Schmit rectangle, of class $C^2$      107 109
Bogner — Fox — Schmit rectangle, of class $C^{k'}$      108
Bouhamidi, A.      53-55
Bramble — Hilbert lemma      201
Brezis, H.      xiv 9-11 34 112
Ciarlet, P.G.      x xv 33 40 66 69—71 87 107 112 132 145 181 201 203
Clamped cubic spline      97
Clement's, operator      75 225
Clement's, result      70 71 107 145 146 149 179 225
Clement, P.      70 71 76
Closed graph theorem      10
Convergence of discrete, interpolating $D^m$-splines      77
Convergence of discrete, smoothing $D^m$-splines      84 147 152 182 184 204 205 226
Convergence of interpolating, $D^m$-splines over ft      67
Convergence of interpolating, (m,l,s)-splines      55
Convergence of interpolating, (m,s)-splines      29
Convergence of smoothing, $D^m$-splines over ft      66 67
Convergence of smoothing, (m,l,s)-splines      56
Convergence of smoothing, (m,s)-splines      40 42
Convergence of smoothing, (m,s)-splines for noisy data      50 52
Craven, P.      x 41 81
Crease      131
Dahmen, W.      ix
Data, hard data      110
Data, Hermite data      111 131 140 147 148
Data, Lagrange data      73 110 114 131 140 147 148 157
Data, of seismic origin      111
Data, orientation data      224
Data, position data      224
de Boor C.      ix
de Rossi, A.      160
de Silanes, Lopez, M.C.      45 47–49 52 55 56 80 87 131 132 160
Deny, J.      6
DIP      111 131 224
Discontinuity, detection      160 163
Discontinuity, set      131-133 148 160
Discrete $D^m$-spline      ix 59 69
Discrete interpolating $D^m$-spline, approximation error      80
Discrete interpolating $D^m$-spline, computation      73 143
Discrete interpolating $D^m$-spline, convergence      77
Discrete interpolating $D^m$-spline, definition      72 142
Discrete interpolating $D^m$-spline, variational characterization      72 142
Discrete smoothing $D^m$-spline, approximation error      87
Discrete smoothing $D^m$-spline, computation      81 107 144 181 223
Discrete smoothing $D^m$-spline, convergence      84 147 152 182 184 204 205 226
Discrete smoothing $D^m$-spline, definition      80 143 152 181 203 223
Discrete smoothing $D^m$-spline, variational characterization      80 143 180 202 223
Discrete space of $D^m$-splines      73
Disk-like surface      220
Duchon, J.      ix 3 5—7 16 20 22 29 31 33 34 36 175
Dyn, N.      ix 26
Extension theorem for Sobolev spaces      xv
fault      131 133
Fault, detection      see “Discontinuity detection”
Fault, line      144 157 160 162
Fault, oblique      131 144
Fault, vertical      131 144 157
Finite element framework      69
Floater, M.S.      132 221 234
Fourier transform      xiii
Franke's function      113
Franke, R.F.      105 113 132
Friedrichs' theorem      8 24 65
Functional spaces, $C^{\mu} (\bar{\Omega})$      xiv
Functional spaces, $C^{\mu} (\bar{\Omega})$, norm on      xiv
Functional spaces, $C_{F}^{k} (\Omega \setminus \bar{F})$      134
Functional spaces, $C_{F}^{k} (\Omega \setminus \bar{F})$, norm on      134
Functional spaces, $H^{l} (\omega, \mathbb{R}^{3})$      219
Functional spaces, $H^{l} (\omega, \mathbb{R}^{3})$, norm on      219
Functional spaces, $H^{m} (\Omega \setminus \bar{F})$      135
Functional spaces, $H^{m} (\Omega \setminus \bar{F})$, norm on      137 146
Functional spaces, $H^{m} (\Omega)$      xiii
Functional spaces, $H^{m} (\Omega)$, norm on      xiii 62 177 204
Functional spaces, $L^{2} (F)$      176
Functional spaces, $L^{2} (F)$, norm on      176
Functional spaces, $X^{m,l,s}$      53
Functional spaces, $X^{m,l,s}$, norm on      54
Functional spaces, $X^{m,s}$      6
Functional spaces, $X^{m,s}$, norm on      8 10 11 28
Functional spaces, $\tilde{H}^{s}$      5
Functional spaces, $\tilde{H}^{s}$, norm on      5
Functions of the Euclidean distance      16
Gaches, J.      61
GCV      see “Generalized cross validation”
Generalized cross validation, function      81 182 224
Generalized cross validation, method      x 41 81 114 161 162 182 189 224 229 235 236 241
Generalized maximum likehood      81
Geymonat, G.      32
Girard, D.      160
Goulaouic, C.      xiv
Gout, C.      199
Gout, J.L.      75
Greiner, G.      221
Grisvard, P.      xiv 31 176
Gu, C.      x 41 81
Gutzmer, T.      160
Hardy, R.L.      21
Hausdorff distance      3 27 67 184
Hollig, K.      ix
Hormander, L.      13 62 65
Hormann, K.      221
Hoschek, J.      235
Hsieh — Clough — Tocher triangle of class $C^1$      110
Hsieh — Clough — Tocher triangle of class $C^2$      110
Hsieh — Clough — Tocher triangle, reduced of class $C^1$      110
Hutchinson, M.F.      82
Hwang, W.L.      160
Index set, $\mathbb{D}$      27 42 55 67 74 145 148 183 204 220
Index set, $\mathbb{E}$      177 199
Index set, $\mathbb{H}$      69 140 145 148 179 202 222
Index set, $\mathscr{E}$      74
Influence matrix      81 182
Interpolating $D^m$-spline over $\Omega$, approximation error      68
Interpolating $D^m$-spline over $\Omega$, convergence      67
Interpolating $D^m$-spline over $\Omega$, definition      61
Interpolating $D^m$-spline over $\Omega$, variational characterization      63
Interpolating (m,l,s)-spline, approximation error      55
Interpolating (m,l,s)-spline, convergence      55
Interpolating (m,l,s)-spline, definition      54
Interpolating (m,l,s)-spline, explicit expression      54
Interpolating (m,s)-spline, approximation error      37
Interpolating (m,s)-spline, computation      25
Interpolating (m,s)-spline, convergence      29
Interpolating (m,s)-spline, definition      13
Interpolating (m,s)-spline, variational characterization      14
Interpolation-smoothing mixed method      110
Inverse assumption      87
Iske, A.      160
Klein, P.      132
Kruth, J.P.      220
Laghchim-Lahlou, M.      110
Lagrange multiplier      14 63 73 112
Lasser, D.      235
Laurent, P.-J.      3 82 95 132 160
Lax — Milgram lemma      40 66 181 203
le Mehaute, A.      53—55 107 132
Lee, D.      160
Levin, D.      26
Lions, J.L.      xiv 6 8 24 65
Lipschitz-continuous boundary      xiv
Local sequential weak compactness theorem      xv
Lodha, S.K.      105
Ma, W.      220
Magenes, E.      xiv 8 24 65
Mallat, S.      160
Manzanilla, R.      105 107 131—133 147
Michelli, C.A.      ix
Minimizing spline      ix
Morrey, C.B.      75
Multiquadric function      21
Natural cubic spline      96
Natural polynomial spline      92
Necas, J.      xiv 3 6 32 47 62 137 176 203 205
Nielson's function      113
Nielson, G.M.      113 132
Non-regular function      131 224
Normalized cubic B-splines      98
Normalized cubic B-splines, basis of      98
Paihua, L.      26
Parameter correction      227 235
Parametrization method      220
Parra, M.C      131 132 160
Pasadas, M.      131 132 225
Peetre, J.      5 185
Phillips, R.      132
Plancherel's Theorem      93
Polyharmonic spline      ix 19
Powell — Sabin triangle      132
Powell — Sabin triangle, of class $C^1$      110
Powell — Sabin triangle, of class $C^2$      110
Powell, M.J.D.      110 132
Prenter, P.M.      99
Pseudo-cubic spline      21
Pseudo-quintic spline      21
Ragozin, D.      52
Raviart, P.-A.      71
Reference surface      221
Regularity, of $D^m$-splines over $\Omega$      65
Regularity, of (m,s)-splines      20
Regularized equation      81
Reimers, M.      221
Relative error      114 228
Rellich — Kondrasov compact imbedding theorem      xiv
Renner, G.      227
Riemenschneider, S.      ix
Rippa, S.      26
Rossini, M.      160
Rozhenko, A.I.      132
Sabin, M.A.      110 132
Sablonniere, P.      110
Sanchez, A.M.      32 33
Schumaker, L.L.      ix 92 95 99
Schwartz, L.      xiii 3 6 7 16 17 19
Scott, L.R.      70
Serres, C.      132
Shape-preserving parametrization method      234
Smoothing $D^m$-spline over $\Omega$, approximation error      68
Smoothing $D^m$-spline over $\Omega$, convergence      66 67
Smoothing $D^m$-spline over $\Omega$, definition      66
Smoothing $D^m$-spline over $\Omega$, variational characterization      66
Smoothing (m,l,s)-spline, approximation error      56
Smoothing (m,l,s)-spline, convergence      56
Smoothing (m,l,s)-spline, definition      55
Smoothing (m,s)-spline, approximation error      49
Smoothing (m,s)-spline, computation      40—41
Smoothing (m,s)-spline, convergence      40 42
Smoothing (m,s)-spline, convergence, for noisy data      50 52
Smoothing (m,s)-spline, definition      39
Smoothing (m,s)-spline, variational characterization      39
Sobolev's continuous imbedding theorem      xv
Sobolev's Holder imbedding theorem      xiv
Space, of $D^m$-splines over $\mathbb{R}$      92
Space, of $D^m$-splines over $\Omega$      64 89 92
Space, of (m,s)-splines      15
Space, of clamped cubic splines      97
Space, of discrete $D^m$-splines      73
Space, of natural cubic splines      96
Space, of natural polynomial splines      92
Splines defined by local mean values, computation      24
Splines defined by local mean values, definition      22
Springer, J.      132
Stampacchia's theorem      112
Strang, G.      32 70 71
Strike      111 131 224
Tarrou, C.      132 144
Theorem, Banach — Steinhaus      34
Theorem, Banach's isomorphism      9 11
Theorem, closed graph      10
Theorem, corollary of Urysohn's      13 62
Theorem, extension theorem for Sobolev spaces      xv
Theorem, Friedrichs'      8 24 65
Theorem, local sequential weak compactness      xv
Theorem, Plancherel's      93
Theorem, Rellich — Kondrasov compact imbedding      xiv
Theorem, Sobolev's continuous imbedding      xv
Theorem, Sobolev's Holder imbedding      xiv
Theorem, Stampacchia's      112
Thin plate spline      ix 20
Tikhonov, A.      81
Torrens, J.J.      107 131—133 147 160 222
Trapezoidal rule      179 188
Treves, F.      xiii
Trial and error      41 81
Uniformity property      71
Univariate $D^m$-spline, explicit expression      89
Univariate $D^m$-spline, interpolating, computation      93
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