对称型Newton-关联连分式混合有理插值

Symmetry Newton-associated Continued Fractions Blending Rational Interpolation

将二元Newton插值与关联连分式插值结合,构造出矩形网格上的对称型Newton-关联连分式混合有理插值,讨论了递推算法,插值定理,并给出误差估计.数值例子说明了文中方法的有效性.文末将结果推广到向量值及矩阵值插值情形和三角网格上的插值。

Both the bivariate Newton interpolation polynomial and related continued fractions are used to construct symmetry Newton-associated continued fractions blending rational interpolation. We discuss the recursive algorithm, interpolating theorem and error estimation, a numerical example is given to show the effectiveness of the method. We extend the conclusion to vector valued, matrix valued case and the triangular net ease.