共查询到17条相似文献,搜索用时 93 毫秒
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二元Thiele型向量有理插值 总被引:19,自引:3,他引:16
本文对二元Thiele型连分式的渐近分式施行Samelson逆变换,建立了平面矩形域上的二元向量值有理插值,所得结果是一元向量值有理插值的推广和改进. 相似文献
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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. 相似文献
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王家正 《应用数学与计算数学学报》2006,20(2):77-82
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. 相似文献
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顾郁枫 《应用数学与计算数学学报》2002,16(2):57-60
本文借助于基于广义逆矩阵Thiele-型连分式插值的计算公式,建立了多项式矩阵求逆的一个新方法。关于多项式矩阵求逆的一个实例给出以说明本文的结果。 相似文献
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关于Newton—Thiele型二元有理插值的存在性问题 总被引:1,自引:1,他引:0
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。 相似文献
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一个二元矩阵插值连分式的展开式 总被引:2,自引:1,他引:1
本文借助于文[1]定义的一种实用的矩阵广义逆,构造了一个二元Stieltjes型矩阵值插值连分式的展开式,它的截断分式可以定义二元矩阵值插值函数. 相似文献
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COMPUTATION OF VECTOR VALUED BLENDING RATIONAL INTERPOLANTS 总被引:3,自引:0,他引:3
檀结庆 《高等学校计算数学学报(英文版)》2003,12(1)
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. 相似文献
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有理插值比多项式插值有更好的近似,但有理插值一般很难控制极点的产生.基于Thiele型连分式插值与重心有理插值,构造三元重心Thiele型混合有理插值,当选取适当的权后能避免部分极点的产生.文章最后通过数值例子验证了这种方法的正确性和有效性. 相似文献
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Bivariate composite vector valued rational interpolation 总被引:5,自引:0,他引:5
In this paper we point out that bivariate vector valued rational interpolants (BVRI) have much to do with the vector-grid to be interpolated. When a vector-grid is well-defined, one can directly design an algorithm to compute the BVRI. However, the algorithm no longer works if a vector-grid is ill-defined. Taking the policy of ``divide and conquer', we define a kind of bivariate composite vector valued rational interpolant and establish the corresponding algorithm. A numerical example shows our algorithm still works even if a vector-grid is ill-defined.
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檀结庆 《高等学校计算数学学报(英文版)》1998,(2)
Efficient algorithms are established for the computation of bivariate lacunary vector valued rational interpolants based on the branched continued fractions and a numerical example is given to show how the algorithms are implemented, 相似文献
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TANJIEQING TANGSHUO 《高校应用数学学报(英文版)》1997,12(1):99-108
Triple branched continued fractions (TBCFs) are constructed by means of well-define Thiele-type partial inverted differences. The characterizatioon theorem, uniqueness theorem andsome projection identity properties are obtained for vector valued rational interpolants hy TBCFs. 相似文献
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Newton-Thiele's rational interpolants 总被引:13,自引:0,他引:13
It is well known that Newton's interpolation polynomial is based on divided differences which produce useful intermediate
results and allow one to compute the polynomial recursively. Thiele's interpolating continued fraction is aimed at building
a rational function which interpolates the given support points. It is interesting to notice that Newton's interpolation polynomials
and Thiele's interpolating continued fractions can be incorporated in tensor‐product‐like manner to yield four kinds of bivariate
interpolation schemes. Among them are classical bivariate Newton's interpolation polynomials which are purely linear interpolants,
branched continued fractions which are purely nonlinear interpolants and have been studied by Chaffy, Cuyt and Verdonk, Kuchminska,
Siemaszko and many other authors, and Thiele-Newton's bivariate interpolating continued fractions which are investigated in
another paper by one of the authors. In this paper, emphasis is put on the study of Newton-Thiele's bivariate rational interpolants.
By introducing so‐called blending differences which look partially like divided differences and partially like inverse differences,
we give a recursive algorithm accompanied with a numerical example. Moreover, we bring out the error estimation and discuss
the limiting case.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献