共查询到18条相似文献,搜索用时 140 毫秒
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本文第一节利用 Samelson逆、混合偏差商以及 Thiele-型分叉连分式构造三元向量值混合有理插值 ,第二节给出了一种计算三元向量值混合有理插值的算法 ,第三节给出了一个数值例子 . 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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基于广义逆的多元矩阵有理插值 总被引:3,自引:1,他引:2
顾传青 《高等学校计算数学学报》1997,19(3):241-250
本文借助于文[5]给出的一种矩阵广义逆,构造了二元Stieltjes型矩阵连分式的截断连分式,以此首次定义了平面上拟三角形网格上的二元矩阵有理插道值函数。文中给出了存在性的一个有用的判别条件。重要的特征定理和唯一性定理得到证明,并借助了实例说明了本文的结果。 相似文献
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三元向量值混合有理插值及其算法 总被引:1,自引:0,他引:1
本第一节利用Samelson逆,混合偏差商以及Thiele-型分叉连分布构造三元向量值混合有理插值,第二节给出了一种计算三元向量值混合有理插值的算法,第三节给出了一个数值例子。 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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一般构造矩阵值有理函数的方法是利用连分式给出的,其算法的可行性不易预知,且计算量大.本文对于二元矩阵值有理插值的计算,通过引入多个参数,定义一对二元多项式:代数多项式和矩阵多项式,利用两多项式相等的充分必要条件通过求解线性方程组确定参数,并由此给出了矩阵值有理插值公式.该公式简单,具有广阔的应用前景. 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
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Qianjin Zhao Jieqing Tan 《高等学校计算数学学报(英文版)》2007,16(1):63-73
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. 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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二元混合连分式展开的混合差商极限方法 总被引:2,自引:0,他引:2
For a univariate function given by its Taylor series expansion,a continuedfraction expansion can be obtained with the Viscovatov's algorithm,as the limitingvalue of a Thiele interpolating continued fraction or by means of the determinantalformulas for inverse and reciprocal differences with coincident data points.In thispaper,both Viscovatov-like algorithms and Taylor-like expansions are incorporatedto yield bivariate blending continued expansions which are computed as the limitingvalue of bivariate blending rational interpolants,which are constructed based on sym-metric blending differences.Numerical examples are given to show the effectivenessof our methods. 相似文献
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A new method for the construction of bivariate matrix valued rational interpolants (BGIRI) on a rectangular grid is presented in [6]. The rational interpolants are of Thiele-type continued fraction form with scalar denominator. The generalized inverse introduced by [3]is gen-eralized to rectangular matrix case in this paper. An exact error formula for interpolation is ob-tained, which is an extension in matrix form of bivariate scalar and vector valued rational interpola-tion discussed by Siemaszko[l2] and by Gu Chuangqing [7] respectively. By defining row and col-umn-transformation in the sense of the partial inverted differences for matrices, two type matrix algorithms are established to construct corresponding two different BGIRI, which hold for the vec-tor case and the scalar case. 相似文献
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《Journal of Computational and Applied Mathematics》1997,84(2):137-146
Bivariate rational interpolating functions of the type introduced in [9, 1] are shown to have a natural extension to the case of rational interpolation of vector-valued quantities using the formalism of Graves-Morris [2]. In this paper, the convergence of Stieltjes-type branched vector-valued continued fractions for two-variable functions are constructed by using the Samelson inverse. Based on them, a kind of bivariate vector-valued rational interpolating function is defined on plane grids. Sufficient conditions for existence, characterisation and uniqueness for the interpolating functions are proved. The results in the paper are illustrated with some examples. 相似文献
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Bivariate blending rational interpolants 总被引:12,自引:0,他引:12
Tan Jieqing 《分析论及其应用》1999,15(2):74-83
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. 相似文献
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Tan Jieqing 《逼近论及其应用》1999,15(2):74-83
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. 相似文献