矩形网格上Lagrange—Thiele型有理插值

Thiele型连分式在有理插值问题中有着重要的应用,它通过定义反差商构造给定结点上的有理函数,其表达式简单、计算方便.现将一元Thiele型连分式与一元Lagrange插值基函数结合起来,构造矩形网格上的Lagrange—Thiele型二元有理插值函数,通过定义偏逆差商,建立递推算法,构造的Lagrange—Thiele型有理插值函数满足有理插值问题中所给的插值条件,并给出了插值的特征定理及对偶性,最后给出数值例子,验证了所给算法的有效性.

Lagrange-Thiele Type Rational Interpolation over Rectangular Grids

Thiele＇ continued fractions have the important application in rational interpolation , which is constructed on the given interpolating points by defining inverse differedces, it is calculated handly and has simple expression. In this paper, Lagrange-Thiele type bivariate rational interpolation has been constructed over rectangular grid based on one dimensional Thiele-continued fractions and combined with the basic function of Lagrange interpolation, by defining partial inverse differences, the recursive algorithm is given . The Lagrange-Thiele rational interpolating function is satisfied with the given interpolating conditions, the characterization theorems of the rational function and duality are carried out. At last, we present a example of this kind of interpolation to illustrate the effectiveness of the interpolating algorithms.