. .. Eléments, 177 6.2.1.3 Construction d'un maillage

. .. Eléments-finis-de-lagrange, , p.181

.. .. Eléments-finis-de-hermite,

. .. Eléments-finis-de-bogner-fox-schmit, , p.185

, Restauration d'images de profondeur par des splines d'interpolation 195

.. .. ,

. .. , 204 7.3.1 Résultats préliminaires pour les familles de changements d'échelle, Construction des changements

.. .. Expérimentations,

. .. Conclusion,

, Rappels et notations

. .. Analyse-fonctionnelle,

?. Relative-À-la-semi-norme-|-·-|-m, opérateur ?, au vecteur ? et au paramètre ? les solutions (si elles existent) ? ? (f ) du problème de minimisation suivant Trouver ? ? (f ) ? H m (?) tel que ?v ? H m (?)

. H-m-(?), La spline d'ajustement ? ? (f ) appartient à l'espace des fonctions splines S introduit en (6.3.11) et est également solution du problème variationnel suivant Trouver ? ? (f ) ? H m (?) tel que ?v ? H m (?) , ? ? ? (f ), ? v R N + ? ? ? (f ), v m,? = ?

, L'espace des fonctions splines S contient donc à la fois les fonctions splines d'interpolation et d'ajustement. Il ne dépend que de la semi-norme | · | m

. Résultats-de-convergence, On s'intéresse dans ce paragraphe à la convergence de l'approximation

, Le premier résultat montre que lorsque ? ? 0, la spline d'ajustement sur ?, ? ? (f ), relative à ?, ? et ? est une approximation de la spline d'interpolation sur ?, ?(f )

. Enfin, on peut montrer que comme dans le cas de l'interpolation, la spline d'ajustement ? ? (f ) converge

. .. Introduction, 196 7.2 Principe général de la méthode d'approximation

. .. , 204 7.3.1 Résultats préliminaires pour les familles de changements d'échelle, Construction des changements

.. .. Expérimentations,

. .. Conclusion,

, On peut montrer que le problème (7.4.4) admet une solution unique appelée spline d'interpolation sur

, Étape 2. La deuxième étape de la démonstration consiste à montrer que toute sous-suite extraite de la famille ? d ? ? d (? d ? f ) d?D , convergeant fortement dans H r?? (?), converge vers la fonction ? ? (? ? f )

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