Nöther-type theorem of piecewise algebraic curves on quasi-cross-cut partition. (English) Zbl 1177.14076

Zhu, ChunGang; Wang, RenHong

Sci. China, Ser. A 52, No. 4, 701-708 (2009).

Summary: Nöther’s theorem of algebraic curves plays an important role in classical algebraic geometry. As the zero set of a bivariate spline, the piecewise algebraic curve is a generalization of the classical algebraic curve. Nöther-type theorem of piecewise algebraic curves is very important to construct the Lagrange interpolation sets for bivariate spline spaces. In this paper, using the characteristics of quasi-cross-cut partition, properties of bivariate splines and results in algebraic geometry, the Nöther-type theorem of piecewise algebraic curves on the quasi-cross-cut is presented.

MSC:

14H99	Curves in algebraic geometry
65D07	Numerical computation using splines
65D18	Numerical aspects of computer graphics, image analysis, and computational geometry

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