Stieltjes-Newton型有理插值

Stieltjes型分叉连分式在有理插值问题中有着重要的地位，它通过定义反差商和混合反差商构造给定结点上的二元有理函数，我们将Stieltjes型分叉连分式与二元多项式结合起来，构造Stieltje- Newton型有理插值函数，通过定义差商和混合反差商，建立递推算法，构造的Stieltjes-Newton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其证明，最后给出的数值例子，验证了所给算法的有效性．

Stieltjes-Newton''''s Rational Interpolants

Stieltjes' branched continued fraction has important position in the problem of multivariate rational interpolation, By defining the inverse difference and blending inverse difference, to structure bivariate rational function which interpolates the given support points. We will incorporate bivariate polynomials in stieltjes' branched continued fraction, Stieltjes-Newton's rational interpolating function is structured, By defining difference and blending inverse difference, and building the recursive algorithm. The rational function satisfies the given interpolating conditions by the problem of rational interpolation, and interpolating characteristical theorem and its proof are given. The end, a numerical example is presented to illustrate the efficiency of this algorithm.