共查询到20条相似文献,搜索用时 93 毫秒
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给出了广义Vandermonde行列式的一种求法,并运用它给出了Lagrange插值公式的几个证明. 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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Lagrange插值公式的几种构造性证明 总被引:4,自引:2,他引:2
利用中国剩余定理、行列式以及线性方程组理论给出了Lagrange插值公式的几种构造性证明,得到了Vandermonde矩阵的逆矩阵的一种算法. 相似文献
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利用经典Lagrange反演公式, 本文给出了一个新的Bell矩阵反演, 由此建立了Bell多项式的一些新的性质, 其中包括一个Bell矩阵反演的封闭形式和经典Fa\`{a} di Bruno公式的一个逆形式. 相似文献
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利用反级数关系构造插值公式的一种方法 总被引:2,自引:0,他引:2
这篇文章指出,互反级数关系可以成为等距插值公式的一个来源。从原则上说来,只要一对互反级数关系中的“求和核”(级数变换核)容许扩充为连续变量的函数,则相应地便可获得一个插值公式。本文举出一系列例子说明了这个方法。特别,我们从广义M?biusRota反演公式出发,造出了一类借助于差分表出的插值公式。这类公式不同于Newton插值法,其特点是具有大范围插值性质;并且由于公式中只使用阶数固定的差分,故还能避免出现“Runge现象”。本文给出了四条定理,论述了这类公式的性质。最后,我们还对具有代数精度的分段(分片) 相似文献
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用构造最优局部逼近空间的方法对Lagrange型四边形单位分解有限元法进行了最优误差分析.单位分解取Lagrange型四边形上的标准双线性基函数,构造了一个特殊的局部多项式逼近空间,给出了具有2阶再生性的Lagrange型四边形单位分解有限元插值格式,从而得到了高于局部逼近阶的最优插值误差. 相似文献
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Xin Rong Ma 《数学学报(英文版)》2002,18(2):289-292
With an effort to investigate a unified approach to the Lagrange inverse Krattenthaler established operator method we finally
found a general pair of inverse relations, called the Krattenthaler forumlas. The present paper presents a very short proof
of this formula via Lagrange interpolation. Further, our method of proof declares that the Krattenthaler result is unique
in the light of Lagrange interpolation.
Received April 9, 1999, Accepted December 7, 2000 相似文献
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Shaochun Chen 《Applied mathematics and computation》2011,217(22):9313-9321
In this paper, using the Newton’s formula of Lagrange interpolation, we present a new proof of the anisotropic error bounds for Lagrange interpolation of any order on the triangle, rectangle, tetrahedron and cube in a unified way. 相似文献
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Jean-Paul Bultel 《Journal of Algebraic Combinatorics》2013,38(2):243-273
We give a new combinatorial interpretation of the noncommutative Lagrange inversion formula, more precisely, of the formula of Brouder–Frabetti–Krattenthaler for the antipode of the noncommutative Faà di Bruno algebra. 相似文献
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1 引 言 本文是讨论关于沿平面代数曲线的Lagrange插值问题,该问题与在二维实平面R~2上的二元Lagrange插值有关.设n为非负整数并且e_n=1/2(n+1)(n_2).P_n代表所有全 相似文献
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《Journal of Computational and Applied Mathematics》2004,163(1):177-187
In this paper, we give a new proof of the famous Cayley–Bacharach theorem by means of interpolation, and deduce a general method of constructing properly posed set of nodes for bivariate Lagrange interpolation. As a result, we generalize the main results in Liang (On the interpolations and approximations in several variables, Jilin University, 1965), Liang and Lü (Approximation Theory IX, Vanderbilt University Press, 1988) and Liang et al. (Analysis, Combinatorics and Computing, Nova Science Publishers, Inc., New York, 2002) to the more extensive situations. 相似文献
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The interpolation polynomials based on Lagrange, Newton and power basis play important roles in applied mathematics, computing method and many other emerging applications. In this paper, we present some coordinate transformation formulae and algorithms as demonstrated below. Firstly, we put forward the formulae of the Lagrange-power basis transformation and its inverse transformation, and as a byproduct, we provide a new method to arrive at the inversion of the Vandermonde matrix. Secondly, we give the formulae of Lagrange-Newton transformation and its inverse transformation. Moreover, we construct related algorithms of Lagrange-power basis transformation, Lagrange-Newton transformation and their inverse transformations. 相似文献
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对多元多项式分次插值适定结点组的构造理论进行了深入的研究与探讨.在沿无重复分量代数曲线进行Lagrange插值的基础上,给出了沿无重复分量分次代数曲线进行分次Lagrane插值的方法,并利用这一结果进一步给出了在R~2上构造分次Lagrange插值适定结点组的基本方法.另外,利用弱Gr(o|¨)bner基这一新的数学概念,以及构造平面代数曲线上插值适定结点组的理论,进一步给出了构造平面分次代数曲线上分次插值适定结点组的方法,从而基本上弄清了多元分次Lagrange插值适定结点组的几何结构和基本特征. 相似文献
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Lawrence A. Harris 《Journal of Mathematical Analysis and Applications》2010,368(1):374-381
Our object is to present an independent proof of the extension of V.A. Markov's theorem to Gâteaux derivatives of arbitrary order for continuous polynomials on any real normed linear space. The statement of this theorem differs little from the classical case for the real line except that absolute values are replaced by norms. Our proof depends only on elementary computations and explicit formulas and gives a new proof of the classical theorem as a special case. Our approach makes no use of the classical polynomial inequalities usually associated with Markov's theorem. Instead, the essential ingredients are a Lagrange interpolation formula for the Chebyshev nodes and a Christoffel-Darboux identity for the corresponding bivariate Lagrange polynomials. We use these tools to extend a single variable inequality of Rogosinski to the case of two real variables. The general Markov theorem is an easy consequence of this. 相似文献