Abstract
The piecewise algebraic curve is a kind generalization of the classical algebraic curve. Nother-type theorem of piecewise algebraic curves on the cross-cut partition is very important to construct the Lagrange interpolation sets for a bivariate spline space. In this paper, using the properties of bivariate splines, the Nother-type theorem of piecewise algebraic curves on the arbitrary triangulation is presented.
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