Cauchy-Vandermonde空间上插值问题的研究

Rational Interpolating In Cauchy-Vandermonde Space

文章首先给出了Cauchy-Vandermonde空间上带极点的有理插值函数的存在唯一性的一种简单证明,建立了带极点的有理插值函数项表达式并给出了其误差估计.进一步推导了CV插值函数的特殊情形——经典Lagrange插值.

We first study the existence and uniqueness of the interpolation by rational functions with prescribed poles in CV space. Then give a new algorithm solving the interpolation problem of multiple nodes and multiple poles, which does not require laborious computation only by solving liner equations. Remainder fonnular also was given. Especially, rational interpolation is classical Lagrange formular.