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Sur la construction de surfaces de classe \(C^ k\) à partir d’un grand nombre de données de Lagrange. (Construction of surfaces of class \(C^ k\) from a large number of Lagrange data). (French) Zbl 0632.65011

The authors approach the problem of effective spline representation of a surface given by a great number of points over a plane domain by using finite elements together with a smoothing operator that yields normal equations that minimize a Sobolev norm, thereby guaranteeing smooth prolongation over the edges of the finite elements while keeping small the dimensions of the linear systems to be solved. They give a convergence proof which yields practical estimates for the small parameters to be used and illustrate their results by some analytic surfaces.
Reviewer: H.Guggenheimer

MSC:

65D10 Numerical smoothing, curve fitting
65D07 Numerical computation using splines
41A15 Spline approximation
41A63 Multidimensional problems
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References:

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