多元分次Lagrange插值

Multivariate Graded Lagrange Interpolation

对多元多项式分次插值适定结点组的构造理论进行了深入的研究与探讨.在沿无重复分量代数曲线进行Lagrange插值的基础上,给出了沿无重复分量分次代数曲线进行分次Lagrane插值的方法,并利用这一结果进一步给出了在R^2上构造分次Lagrange插值适定结点组的基本方法.另外,利用弱Gr(o|¨)bner基这一新的数学概念,以及构造平面代数曲线上插值适定结点组的理论,进一步给出了构造平面分次代数曲线上分次插值适定结点组的方法,从而基本上弄清了多元分次Lagrange插值适定结点组的几何结构和基本特征.

The constitution theory of a properly posed set of nodes for the multivariate polynomial graded interpolation is studide deeply in this paper.on the basis of Lagrange interpolation which along the algebraic curve without multiple factors, we give the approach of graded Lagrange interpolation which along the algebraic curve without multiple factors. Futhermore, using this result we give a basic method to construct the graded Lagrange interpolation in R2. In addition, using weakGroebner basis method which is a new mathematic concept, we give the method to construct the properly posed set of nods for graded interpolation on plane algebraic curve accordingly. Therefore we make clear the geometrical structure of properly posed set of nodes for graded interpolation basically.