共查询到18条相似文献,搜索用时 78 毫秒
1.
最简型的Hermite插指 总被引:2,自引:1,他引:1
颜宁生 《应用数学与计算数学学报》2006,20(1):75-81
本文提出了Hermite插值问题的一种新形式,幂指数形式,简称Hermite插指。 相似文献
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牛顿(Newton)插指 总被引:5,自引:0,他引:5
提出了牛顿(Newton)插值问题的一种新形式,幂指数形式,简称牛顿插指.应用这种插指法,可以容易构造出一类离散型总体的一种公式式分布律. 相似文献
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给出一种基于商的形式的Lagrange与Hermite插值公式及其证明,同时还给出了两个相关的不等式. 相似文献
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振荡函数的Hermite数值积分公式 总被引:3,自引:0,他引:3
本文讨论了振荡函数形如∫-1^1 f(x)sinwxdx,∫-1^1 f(x)coswxdx的Hermite积分公式,它基于f(x)的Hermite插值多项式的一些结论,导出了依赖于xnj的am1及不依赖于xn1的g(k,w)的权数因子的递推关系式,并给出误差分析。 相似文献
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插值算子逼近是逼近论中一个非常有趣的问题,尤其是以一些特殊的点为结点的插值算子的逼近问题很受人们的关注.研究了以第一类Chebyshev多项式零点为插值结点的Hermite插值算子在Orlicz范数下的逼近. 相似文献
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本文研究一类 Hermite 插值基函数在空间 E~p(D-),p>1上的不完备性,其闭包的特征性质以及在此空间中的双正交展开的求和问题. 相似文献
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提出了Gauss插指算子的概念,利用Gauss插指算子得到了2n 1阶Gauss前向插指公式,给出了应用该公式的例子. 相似文献
9.
Hermite插值多项式在不同基下的显式表示 总被引:5,自引:0,他引:5
本利用对偶基的概念,导出了Hermite插值多项式在不同基下的显式表示,这给人们对Hermit插值多项式在不同基下从一种表示转换到另一种表示带来极大的方便。 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
11.
A. Le Méhauté 《Advances in Computational Mathematics》2000,12(4):311-333
The purpose of this paper is to present some aspects of multivariate Hermite polynomial interpolation. We do not focus on
algebraic considerations, combinatoric and geometric aspects, but on explicitation of formulas for uniform and non-uniform
bivariate interpolation and some higher dimensional problems. The concepts of similar and equivalent interpolation schemes
are introduced and some differential aspects related to them are also investigated.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
12.
We present formulas for the divided differences of the remainder of the interpolation polynomial that include some recent interesting formulas as special cases. 相似文献
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In this work we propose three different procedures for vector-valued rational interpolation of a function F(z), where , and develop algorithms for constructing the resulting rational functions. We show that these procedures also cover the general case in which some or all points of interpolation coalesce. In particular, we show that, when all the points of interpolation collapse to the same point, the procedures reduce to those presented and analyzed in an earlier paper (J. Approx. Theory 77 (1994) 89) by the author, for vector-valued rational approximations from Maclaurin series of F(z). Determinant representations for the relevant interpolants are also derived. 相似文献
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Avram Sidi 《Journal of Approximation Theory》2008,(2):75-96
In a recent paper of the author [A. Sidi, A new approach to vector-valued rational interpolation, J. Approx. Theory 130 (2004) 177–187], three new interpolation procedures for vector-valued functions F(z), where F:C→CN, were proposed, and some of their algebraic properties were studied. One of these procedures, denoted IMPE, was defined via the solution of a linear least-squares problem. In the present work, we concentrate on IMPE, and study its convergence properties when it is applied to meromorphic functions with simple poles and orthogonal vector residues. We prove de Montessus and Koenig type theorems when the points of interpolation are chosen appropriately. 相似文献
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Xing-hua WANG Department of Mathematics Zhejiang University Hangzhou China 《中国科学A辑(英文版)》2007,50(11):1651-1660
Explicit representations for the Hermite interpolation and their derivatives of any order are provided.Furthermore,suppose that the interpolated function f has continuous derivatives of sufficiently high order on some sufficiently small neighborhood of a given point x and any group of nodes are also given on the neighborhood.If the derivatives of any order of the Hermite interpolation polynomial of f at the point x are applied to approximating the corresponding derivatives of the function f(x),the asymptotic representations for the remainder are presented. 相似文献
17.
Y. G. Zhang 《分析论及其应用》2016,32(1):65-77
General interpolation formulae for barycentric interpolation and barycentric rational Hermite interpolation are established by introducing multiple parameters,which include many kinds of barycentric interpolation and barycentric rational Hermite interpolation. We discussed the interpolation theorem, dual interpolation and special cases. Numerical example is given to show the effectiveness of the method. 相似文献