二元双n次多项式插值问题研究

Researches on binary double n degree polynomial interpolation

以构造二元插值正则结点组的方法为研究基础,对二元双n次代数多项式插值正则性问题进行了详尽的研究和探讨.搞清了二元双n次插值正则结点组的基本拓扑结构和几何特征,并给出了构造二元双n次插值多项式空间及沿二元双n次代数曲线插值正则结点组的迭加构造法,最后通过两个实验算例对所得研究结果进行了验证.

Based on the method of constructing binary interpolation regular node group,we researched the interpolation regularity problem of binary double n degree algebraic polynomials.In this paper,we have basically understood the basic topological structure and geometric features of the binary double n degree interpolation regular node group.Then we employed a superposition method to construct binary double n degree interpolation polynomial space and a set of interpolated regular nodes along binary double n degree algebraic curve.Finally,the results are verified by two experimental examples.