三元混合有理插值

Triple blending rational interpolants

在一元、二元情形中 ,差商和偏逆差商分别在构造线性和非线性插值中扮演重要角色。值得注意的是 Newton插值多项式和 Thiele-型插值分叉连分式能用类似于张量积的方法结合在一起去产生一种三元插值方法。文章主要研究三元混合有理插值。通过引入所谓的混合偏差商 ,给出一个递推算法及一个数值例子 。

In the univariate and bivariate cases, divided differences and partial inverted differences play important roles in constructing linear and nonlinear interpolants respectively. It is interesting to notice that Newton's interpolation polynomials and Thiele-type interpolating branched continued fractions can be incorporated in tensor-product-like manner to yield a kind of triple interpolation scheme. In this paper, emphasis is put on the study of triple blending rational interpolants. By introducing the so-called blending partial differences,a recursive algorithm is given as well as a numerical example. The characteristic theorem and an error estimation are also presented.