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Zbl 0632.65011
Apprato, D.; Arcangeli, R.; Manzanilla, R.
Sur la construction de surfaces de classe $C\sp k$ à partir d'un grand nombre de données de Lagrange. (Construction of surfaces of class $C\sp k$ from a large number of Lagrange data). (French)
[J] RAIRO, Modélisation Math. Anal. Numér. 21, 529-555 (1987). ISSN 0764-583X

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.
[H.Guggenheimer]

MSC 2000:: *65D10 Smoothing
65D07 Splines (numerical methods)
41A15 Spline approximation
41A63 Multidimensional approximation problems

Keywords: Lagrange data; fitting; smoothing spline; numerical examples; surface; finite elements; smoothing operator; normal equations; smooth prolongation; convergence

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Zentralblatt MATH Berlin [Germany]