Tensor-product spline interpolation to data on or near a family of lines
type: Item
instance of: scholarly article
title: Tensor-product spline interpolation to data on or near a family of lines
zbMATH Open document ID: 0798.65015
DOI: 10.1007/BF02210502
author: I. J. Anderson
author: Maurice Cox
author: J. C. Mason
published in: Numerical Algorithms
publication date: 1994-10-30T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 510199
zbMATH Keywords: tensor-product spline
zbMATH Keywords: family of parallel lines
zbMATH Keywords: direct algorithms
zbMATH Keywords: spline interpolation
reviewed by: H. P. Dikshit
MaRDI profile type: Publication
cites work: Q4726771
cites work: Curve and Surface Fitting
cites work: An Algorithm for Spline Interpolation
cites work: Q4740951
Recommended article: Q4336244
Recommended article: Q4242869
Recommended article: Q4378615
Recommended article: Q3473589
Recommended article: Q4945654
Recommended article: Tensor product polynomial splines
Recommended article: Q4249852
Recommended article: A new family of convex splines for data interpolation
description: scientific article; zbMATH DE number 510199