Geodesic
Interpolation on a square with a minimum value of the uniform norm of the Laplace operator
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 4, pp. 249-257 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the problem of interpolation of finite sets of numerical data by smooth functions that are defined on a plane square and vanish on its boundary. Under some constraints on the location of interpolation points inside the square, we obtain two-sided estimates with a correct dependence on the number of interpolation points for the $L_\infty$-norms of the Laplace operator of the best interpolants. For the case of interpolation at one point, which is the center of the square, we find an exact solution.
Mots-clés : interpolation
Keywords: Laplace operator, cubic $B$-splines. 
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S. I. Novikov. Interpolation on a square with a minimum value of the uniform norm of the Laplace operator. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 4, pp. 249-257. http://geodesic.mathdoc.fr/item/TIMM_2012_18_4_a21/

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