Tensor-product spline interpolation to data on or near a family of lines
Algorithms for tensor-product spline approximation (in the sense of least squares) to data of the following types: (a) values on a rectangular mesh, (b) values on a family of parallel lines and (c) data that is generally scattered are known already [see for example, \textit{M. G. Cox} [Inst. Math. Appl. Conf. Ser., New Ser. 9, 111-138 (1987; Zbl 0615.65007)]. However direct algorithms for tensor-product spline interpolation are available only for data of type (a). In this paper the authors extend the range of solvable spline interpolation problems by describing how tensor-product spline interpolants can be constructed efficiently and directly for type (b) data. It is also shown that in case (c) when the data lies close to a family of parallel lines, iterative application of the foregoing approach for type (b) can be used to provide an interpolant.
scientific article; zbMATH DE number 510199