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矩形网格上二元向量有理插值的对偶性 总被引:18,自引:0,他引:18
矩形网格上二元向量有理插值的对偶性朱功勤,檀结庆(合肥工业大学)THEDUALITYOFBIVSRIATEVECTORVALUEDRATIONALINTERPOLANTSOVERRECTANGULARGRIDS¥ZhuGong-qin;TanJie-... 相似文献
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Chuan-qing Gu 《计算数学(英文版)》2002,(2)
1. IntroductionWynn [11] proposed a method for rational interpolation of vector-vaued quantities givenon a set of distinct illterpolation points. He used colltinued fractions and generalized inversesfor the reciproca1 of vector-vaued qualltities. McCleod … 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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By making use of Thiele-type bivariate branched continued fractions and Sumelson inverse,we construct a few kinds of bivariate vector valued rational interpolonts (BVRIs) over rectangular grids and find out certain relations among these BVRIs such as boundary identity and duality. 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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二元Thile型向量有理插值的误差公式 总被引:1,自引:0,他引:1
借助于Somelson广义逆,文[1]首次讨论了多元向量有理插值问题.本文得到了二元Thiele型向量有理插值的一个精确的误差公式. 相似文献
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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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At present, the methods of constructing vector valued rational interpolation function in rectangular mesh are mainly presented by means of the branched continued fractions. In order to get vector valued rational interpolation function with lower degree and better approximation effect, the paper divides rectangular mesh into pieces by choosing nonnegative integer parameters d1 (0 〈 dl ≤ m) and d2 (0 ≤ d2≤ n), builds bivariate polynomial vector interpolation for each piece, then combines with them properly. As compared with previous methods, the new method given by this paper is easy to compute and the degree for the interpolants is lower. 相似文献
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预给极点的向量有理插值及性质 总被引:3,自引:1,他引:2
1 引 言在工程技术中经常会遇到一些多元奇异函数的计算问题,常规的有理插值方法无疑为这类问题的近似求解提供了有效的途径,但有时逼近效果不一定十分理想,其重要原因之一是人们往往采用统一的框架去构造有理插值公式,而忽略了被逼近对象的一些本质特征.针对某些具体问题,例如已知被逼近的向量值函数的奇异点的有关信息,构造一种预给极点的向量有理插值格式就显得很有必要,其逼近效果自然会更理想.设R2中的点集Πn,m={(xi,yj)|i=0,1,…,n;j=0,1,…,m},相应的d维向量集Vn,m={Vi,j∈Cd|i=0,1,…,n;j=0,1,…,m}.设V∈Cd为任一d维… 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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Graves-Morris于1983年利用向量的Samelson逆变换建立了一种实用的向量有理插值方法。本文得到了该向量有理插值的一个精确的误差公式。 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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二元切触有理插值是有理插值的一个重要内容,而降低其函数的次数和解决其函数的存在性是有理插值的一个重要问题.二元切触有理插值算法的可行性大都是有条件的,且计算复杂度较大,有理函数的次数较高.利用二元Hermite(埃米特)插值基函数的方法和二元多项式插值误差性质,构造出了一种二元切触有理插值算法并将其推广到向量值情形.较之其它算法,有理插值函数的次数和计算量较低.最后通过数值实例说明该算法的可行性是无条件的,且计算量低. 相似文献
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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