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Local recovery of a solenoidal vector field by an extension of the thin- plate spline technique. (English) Zbl 0790.65009

The author shows how one can interpolate a vector-valued function in two or three dimensions, whose value is (wholly or partly) known at a sufficient (but not large) number of points disposed in almost any configuration, under the condition that the interpolating function has zero divergence. The technique is based on the theory of thin plate splines. The author demonstrates an easily-implemented technique for interpolating scattered velocity components by a solenoidal vector field that is, in a well-defined sense, optimal.
Reviewer: R.S.Dahiya (Ames)

MSC:

65D07 Numerical computation using splines
65D05 Numerical interpolation
41A05 Interpolation in approximation theory
41A63 Multidimensional problems
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References:

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