COMPUTATION OF VECTOR VALUED BLENDING RATIONAL INTERPOLANTS

As we know, Newton's interpolation polynomial is based on divided differences which can be calculated recursively by the divided-difference scheme while Thiele 's interpolating continued fractions are geared towards determining a rational function which can also be calculated recursively by so-called inverse differences. In this paper, both Newton's interpolation polynomial and Thiele's interpolating continued fractions are incorporated to yield a kind of bivariate vector valued blending rational interpolants by means of the Samelson inverse. Blending differences are introduced to calculate the blending rational interpolants recursively, algorithm and matrix-valued case are discussed and a numerical example is given to illustrate the efficiency of the algorithm.     

一种新形式的二元混合有理插值(英文)

Newton＇s polynomial interpolation may be the favorite linear interpolation,associated continued fractions interpolation is a new type nonlinear interpolation.We use those two interpolation to construct a new kind of bivariate blending rational interpolants.Characteristic theorem is discussed.We give some new blending interpolation formulae.     

关于Newton—Thiele型二元有理插值的存在性问题

基于均差的牛顿插值多项式可以递归地实现对待插值函数的多项式逼近,而Thiele型插值连分式可以构造给定节点上的有理函数。将两者结合可以得到Newton-Thiele型二元有理插值（NTRI）算法,本文解决了NTRI算法的存在性问题,并有数值例子加以说明。     

Block Based Bivariate Blending Rational Interpolation via Symmetric Branched Continued Fractions

This paper constructs a new kind of block based bivariate blending rational interpolation via symmetric branched continued fractions. The construction process may be outlined as follows. The first step is to divide the original set of support points into some subsets (blocks). Then construct each block by using symmetric branched continued fraction. Finally assemble these blocks by Newton’s method to shape the whole interpolation scheme. Our new method offers many flexible bivariate blending rational interpolation schemes which include the classical bivariate Newton’s polynomial interpolation and symmetric branched continued fraction interpolation as its special cases. The block based bivariate blending rational interpolation is in fact a kind of tradeoff between the purely linear interpolation and the purely nonlinear interpolation. Finally, numerical examples are given to show the effectiveness of the proposed method.     

Bivariate blending rational interpolants

Both the Newton interpolating polynomials and the Thiele-type interpolating continued fractions based on inverse differences are used to construct a kind of bivariate blending rational interpolants and an error estimation is given.     

Bivariate blending rational interpolants

Both the Newton interpolating polynomials and the Thiele-type interpolating continued fractions based on inverse differences are used to construct a kind of bivariate blending rational interpolants and an error estimation is given.     

三元New ton-Thiele型插值方法

本文以 Newton插值及 Thiele型连分式插值为基础 ,将线性与非线性插值方法相结合 ,通过混合差商的定义 ,给出了三元 Newton-Thiele型插值公式及误差估计式 .     

基于二元连分式的散乱数据递推插值格式

本文首先基于新的非张量积型偏逆差商递推算法,分别构造奇数与偶数个插值节点上的二元连分式散乱数据插值格式,进而得到被插函数与二元连分式间的恒等式.接着,利用连分式三项递推关系式,提出特征定理来研究插值连分式的分子分母次数.然后,数值算例表明新的递推格式可行有效,同时,通过比较二元Thiele型插值连分式的分子分母次数,发现新的二元插值连分式的分子分母次数较低,这主要归功于节省了冗余的插值节点. 最后,计算此有理函数插值所需要的四则运算次数少于计算径向基函数插值.     

QD-Type algorithms for the nonnormal Newton-Padé approximation table

It is well known that solutions of the rational interpolation problem or Newton-Padé approximation problem can be represented with the help of continued fractions if certain normality assumptions are satisfied. By comparing two interpolating continued fractions, one obtains a recursive QD-type scheme for computing the required coefficients. In this paper a uniform approach is given for two different interpolating continued fractions of ascending and descending type, generalizing ideas of Rutishauser, Gragg, Claessens, and others. In the nonnormal case some of the interpolants are equal yielding so-called singular blocks. By appropriate “skips” in the Newton-Padé table modified interpolating continued fractions are derived which involve polynomials known from the Kronecker algorithm and from the Werner-Gutknecht algorithm as well as from the modification of the cross-rule proposed recently by the authors. A corresponding QD-type algorithm for the nonnormal Newton-Padé table is presented. Finally, the particular case of Padé approximation is discussed where—as in Cordellier's modified cross-rule—the given recurrence relations become simpler.     

Lagrange基函数的复矩阵有理插值及连分式插值

1引言 矩阵有理插值问题与系统线性理论中的模型简化问题和部分实现问题有着紧密的联系~[1][2]，在矩阵外推方法中也常常涉及线性或有理矩阵插值问题~[3]。按照文~[1]的阐述。目前已经研究的矩阵有理插值问题包括矩阵幂级数和Newton-Pade逼近。Hade逼近，联立Pade逼近，M-Pade逼近，多点Pade逼近等。显然，上述各种形式的矩阵Pade逼上梁山近是矩