Approximation by cubic \(C^ 1\)-splines on arbitrary triangulations
type: Item
instance of: scholarly article
title: Approximation by cubic \(C^ 1\)-splines on arbitrary triangulations
zbMATH Open document ID: 0595.41010
DOI: 10.1007/BF01399695
author: B. George
published in: Numerische Mathematik
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133185
review text: We present an efficient global representation for bivariate piecewise cubic splines of class \(C^ 1\) on arbitrary triangulations. The polynomial pieces of the splines on the different triangles are uniquely determined by a minimal number of real-valued parameters. The \(C^ 1\)- smoothness of the splines is ensured by imposing a linear equation on the parameters for every interior edge in the triangulation. The considerable saving in the amount of stored information makes this representation attractive for practical computations. A numerical method is discussed for computing the dimension of the space of these splines. Furthermore, we consider subspaces of splines satisfying certain boundary conditions. Some applications are given where piecewise cubic \(C^ 1\)-functions are used to solve practical approximation problems, such as the interpolation to data in combination with the minimization of the thin plate functional and the least-squares approximation of scattered data.
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 65D07
zbMATH DE Number: 3957865
zbMATH Keywords: bivariate piecewise cubic splines
zbMATH Keywords: \(C^ 1\)-smoothness
zbMATH Keywords: numerical method
zbMATH Keywords: least-squares approximation of scattered data
zbMATH Keywords: spline space
describes a project that uses: symrcm
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3957865