共查询到18条相似文献,搜索用时 550 毫秒
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1 引言
一元向量值有理插值问题在[1-5]中有了比较系统的研究.文[6—13]成功地将一无的结果推广到了二元的情形,但它们采用的大多是向量值连分式的方法,且没有给出二元向量值有理插值存在性的判别方法及其证明.本文利用二元Newton插值公式, 相似文献
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向量值有理插值存在性的一种判别方法 总被引:3,自引:1,他引:2
对于向量值有理插值的计算,目前已经有多种求解算法.但其存在性的判别方法及其证明在现有的文献中还没有见到.这里利用标量有理插值函数插值存在性的思想,引入Newton基函数,给出并证明了向量值有理插值存在性的一种判别方法.同时给出有理插值函数的分子和分母的显式表达式,最后的实例说明了它的有效性. 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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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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切触有理插值是函数逼近的一个重要内容,而降低切触有理插值的次数和解决切触有理插值函数的存在性是有理插值的一个重要问题.切触有理插值函数的算法大都是基于连分式进行的,其算法可行性是有条件的,且计算量较大.利用Newton(牛顿)多项式插值的承袭性和分段组合的方法,构造出了一种无极点且满足高阶导数插值条件的切触有理插值函数,并推广到向量值切触有理插值情形;既解决了切触有理插值函数存在性问题,又降低了切触有理插值函数的次数.最后给出误差估计,并通过数值实例说明该算法具有承袭性、计算量低、便于编程等特点. 相似文献
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在用广义Vandermonde行列式给出Hermite插值多项式的表达式的基础上,针对a<,i>=2(i=1,2,…,s)的情形给出向量值切触有理插值存在性问题有解的条件及表达式. 相似文献
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一种求二元有理插值函数的方法 总被引:11,自引:3,他引:8
给出一种方法可直接计算基于矩形节点的二元有理插值函数的分母在节点处的值 ,进而判断相应的二元有理插值函数是否存在 .此方法运用灵活 ,适用范围广 ,在相应的有理插值函数存在时 ,能给出它的具体表达式 .此外 ,我们还针对文中两个主要逆矩阵 ,给出了相应的递推公式 ,避免了求逆计算 . 相似文献
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矩阵有理插值及其误差公式 总被引:24,自引:1,他引:24
矩阵有理插值及其误差公式顾传青,陈之兵(合肥工业大学)MATRIXVALUEDRATIONALINTERPOLANTSANDITSERRORFORMULA¥GuChuan-qing;ChenZhi-bing(HefeiUniversityofTech... 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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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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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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In 1963, Wynn proposed a method for rational interpolation of vector-valued quantities given on a set of distinct interpolation points. He used continued fractions, and generalized inverses for the reciprocals of vector-valued quantities. In this paper, we present an axiomatic approach to vector-valued rational interpolation. Uniquely defined interpolants are constructed for vector-valued data so that the components of the resulting vector-valued rational interpolant share a common denominator polynomial. An explicit determinantal formula is given for the denominator polynomial for the cases of (i) vector-valued rational interpolation on distinct real or complex points and (ii) vector-valued Padé approximation. We derive the connection with theε-algorithm of Wynn and Claessens, and we establish a five-term recurrence relation for the denominator polynomials. 相似文献
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ZhibingChen 《计算数学(英文版)》2003,21(2):157-166
A new kind of matrix-valued rational interpolants is recursively established by means of generalized Samelson iverse for matrices,with scalar numerator and matrix-valued denominatror.In this respect,it is essentially different form that of the previous works [7,9],where the matrix-valued rational interpolants is in Thiele-type continued fraction form with matrix-valued numerator and scalar denominator.For both univariate and bivariate cases,sufficient conditions for existence,characterisation and univquenese in some sense are proved respectively,and an error formula for the univariate interpolating function is also given.The results obtained in this paper are illustrated with some numerical examples. 相似文献