Abstract
Algorithms exist for least-squares tensor-product splineapproximation to data (a) on a rectangular mesh, (b) on a family of parallel lines and (c) that is generally scattered. In contrast,direct algorithms for tensor-product splineinterpolation are available only for data type (a). The structure of the data in cases (a) and (b) is such that the corresponding algorithms are particularly efficient.
This paper extends the range of solvable spline interpolation problems by describing how tensor product spline interpolants can be constructed efficiently and directly for data type (b). Moreover, for a limited class of data of type (c), viz. when the data liesclose to a family of parallel lines, it is shown that iterative application of our approach for data type (b) can be used to provide an interpolant.
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Anderson, I.J., Cox, M.G. & Mason, J.C. Tensor-product spline interpolation to data on or near a family of lines. Numer Algor 5, 193–204 (1993). https://doi.org/10.1007/BF02210502
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DOI: https://doi.org/10.1007/BF02210502