Grid Point Interpolation on Finite Regions Using C1 Box Splines

Multivariate grid point interpolation on finite regions is considered by translates of C1 box splines defined on a (s + 1)-direction mesh in Rs. In general, this problem will give more degrees of freedom than the number of interpolation conditions, and hence the problem has no unique solution. Among...

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Bibliographic Details
Published in:SIAM journal on numerical analysis 1992-08, Vol.29 (4), p.1136-1153
Main Authors: Arge, Erlend, Daehlen, Morten
Format: Article
Language:English
Subjects:
Applied mathematics
Approximation
Cubes
Exact sciences and technology
Interpolation
Linear equations
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Polynomials
Rectangles
Sciences and techniques of general use
Tensors
Uniqueness
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Summary:Multivariate grid point interpolation on finite regions is considered by translates of C1 box splines defined on a (s + 1)-direction mesh in Rs. In general, this problem will give more degrees of freedom than the number of interpolation conditions, and hence the problem has no unique solution. Among all interpolants, the one minimizing a smoothing functional is chosen. Two choices of the smoothing functional are proposed, and the related existence and uniqueness problems are studied. Examples showing constructions of box spline surfaces on nonrectangular regions in R2 and rectangular regions in R3 are presented. The method can also be used to construct a smooth interpolant to a set of points given at an almost arbitrary set of grid points in Rs.
ISSN:0036-1429
1095-7170