关于多元插值适定性问题研究

Some Researches on Properly for Multrivariate Interpolation

本文以代数几何中某些理论方法为工具,对三元Lagrange插值适定性问题进行了研究和探讨.文中将文献[1]中所给出的构造沿曲面多元函数插值适定结点组的添加平面法加以推广,得到了新的构造方法-添加曲面法和添加空间代数曲线法.这些方法不仅可以保证插值函数的存在与唯一性,而且还便于求得具体插值公式.同时,该方法也扩展了文献[2,3]中给出的构造沿单位圆盘及单位球面插值适定结点组的几种方法.

In this paper,using some methods and theories in algebraic geometry as tool,the problem of properly for trivariate Lagrange Interpolation is researched and approached.The plane-superposed process which was given in [1] for constructing properly posed set of nodes of trivariate Lagrange interpolation along a surface is generalized to some new method,i.e.,the surface-superposed process and space curve-superposed process whose assure not only the existence and uniqueness of the interpolation function,but the schemes of interpolation could be acquired conveniently.At the same time,those methods also expands some results in for constructing properly posed set of nodes of interpolation along the unit disk and the unit sphere.