Lagrange interpolation by bivariate splines on cross-cut partitions

Authors:
Chun-Gang Zhu;Ren-Hong Wang
Affiliations:
Institute of Mathematical Sciences, Dalian University of Technology, Dalian, China;Institute of Mathematical Sciences, Dalian University of Technology, Dalian, China
Venue:
Journal of Computational and Applied Mathematics - Special issue: The international symposium on computing and information (ISCI2004)
Year:
2006

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Abstract

The piecewise algebraic curve is a generalization of the classical algebraic curve. In this paper, we give the Nöther-type theorem of piecewise algebraic curves on cross-cut partitions. By using interpolation along a piecewise algebraic curve, we also present a method to construct Lagrange interpolation sets for bivariate spline spaces on cross-cut partitions.