Approximation of vectors fields by thin plate splines with tension

Authors:
M. N. Benbourhim;A. Bouhamidi
Affiliations:
Laboratoire MIP-UMR 5640, Université Paul Sabatier, UFR MIG, 118, route de Narbonne, F-31062 Toulouse Cedex 04, France;L.M.P.A, Université du Littoral Côte d'Opale, 50 rue F. Buisson BP699, F-62228 Calais Cedex, France
Venue:
Journal of Approximation Theory
Year:
2005

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Abstract

We study a vectorial approximation problem based on thin plate splines with tension involving two positive parameters: one for the control of the oscillations and the other for the control of the divergence and rotational components of the field. The existence and uniqueness of the solution are proved and the solution is explicitly given. As special cases, we study the limit problems as the parameter controlling the divergence and the rotation converges to zero or infinity. The divergence-free and the rotation-free approximation problems are also considered. The convergence in Sobolev space is studied.