逆差商的一个紧凑行列式表示(英文)

A Compact Determinantal Representation for Inverse Difference

英文关键词:inverse difference  reciprocal difference  determinant.

中文摘要:

      本文给出了逆差商的一个紧凑行列式表示，从该表示式易知，一个函数在某ｎ＋１个点的ｎ阶逆差商与这些点的排序有关，但与前ｎ－１个点的局部换序无关．此外，还从另一角度定义倒差商，得出了倒差商与逆差商之间的关系以及倒差商的整体换序无关性．

英文摘要:

      A compact determinantal representation for inverse difference is given. From the representation it is easy to know that the inverse difference of a function at some n + 1 points x₀, x₁, x_n depends on th orderings of these points and it is locally independent of the permutation of first n - 1 points. Moreover we define reciprocal difference from another point of view, get the relation between inverse difference and reciprocal difference and obtain the property that the reciprocal difference is globally independent of the permutation of the points.