共查询到20条相似文献,搜索用时 46 毫秒
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1 引言 Birkhoff三角插值是近年来比较活跃的一个研究课题,涉及Birkhoff三角插值的研究文献也很多(如G.G.Lorentz~([1]),沈燮昌~([2])等综合性文章). 相似文献
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The chromatic polynomial PG(q) of a loopless graph G is known to be non-zero (with explicitly known sign) on the intervals (−∞,0), (0,1) and (1,32/27]. Analogous theorems hold for the flow polynomial of bridgeless graphs and for the characteristic polynomial of loopless matroids. Here we exhibit all these results as special cases of more general theorems on real zero-free regions of the multivariate Tutte polynomial ZG(q,v). The proofs are quite simple, and employ deletion–contraction together with parallel and series reduction. In particular, they shed light on the origin of the curious number 32/27. 相似文献
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在构造拉格朗日插值算法时,插值结点的选择是十分重要的.给定一个足够光滑的函数,如果结点选择的不好,当插值结点个数趋于无穷时,插值函数不收敛于函数本身.例如龙格现象:对于龙格函数f(x)=1/1+25x^2,如果拉格朗日插值的结点取[-1,1]上的等距结点,那么逼近的误差会随着结点个数增多而趋于无穷大⑴,由此可知插值结点的选择尤为重要. 相似文献
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High dimensional polynomial interpolation on sparse grids 总被引:2,自引:0,他引:2
Barthelmann Volker Novak Erich Ritter Klaus 《Advances in Computational Mathematics》2000,12(4):273-288
We study polynomial interpolation on a d-dimensional cube, where d is large. We suggest to use the least solution at sparse grids with the extrema of the Chebyshev polynomials. The polynomial
exactness of this method is almost optimal. Our error bounds show that the method is universal, i.e., almost optimal for many
different function spaces. We report on numerical experiments for d = 10 using up to 652 065 interpolation points.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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《佛山科学技术学院》2014,6(4):427-434
In this paper, a new scheme is proposed to find the fuzzy interpolation polynomial. In this case, the nodes are crisp data and the values are fuzzy numbers. In order to obtain the interpolation polynomial, a linear system is solved with crisp coefficients matrix and fuzzy right hand side. Then, the inherited lower-upper (LU) triangular factorization and inherited interpolation are applied to solve this system. The examples illustrate the applicability, simplicity and efficiency of the proposed method. 相似文献
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Ezio Venturino 《Advances in Computational Mathematics》1994,2(2):223-233
Here, the following lacunary interpolation problem is considered: to find the polynomial which together with its second and
third derivatives agrees on arbitrary points with the corresponding values of a given function. The representation of the
polynomial depends on the solution of a linear algebraic system. The method is constructed on this observation. The error
analysis shows that it behaves like the corresponding Lagrange interpolation problem with an equivalent number of conditions.
Some applications are shown. 相似文献
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Tianzi Jiang 《BIT Numerical Mathematics》1995,35(4):540-547
In this paper we introduce a new kind of Birkhoff type interpolation of functions with period 2. We find necessary and sufficient conditions for regularity of this new interpolation problem. Moreover, a closed form expression for the interpolation polynomial is given.This work was supported by China State Major Key Project for Basic Researchers. 相似文献
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The disadvantage of the extension of the Davidon-Fletcher-Powell method to infinite-dimensional space is that the information to be stored in the computer increases with the number of iterations. In this paper, a computational scheme is proposed to remove this disadvantage and make the extension method more practicable. The linear operator which determines the direction of one-dimensional search in the method is formulated by integral kernels to derive the scheme. Furthermore, polynomial interpolation methods are proposed to save computer storage. The computational scheme which is presented here and the polynomial interpolation method are successfully applied to an optimal control problem.The authors would like to thank Dr. N. Adachi for valuable discussion. Computations were carried out at the computing centers of Osaka University, Kyoto University, and Tokyo University. 相似文献
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本文给出了巴拿赫空间中线性差分方程的两个多项式二分性概念, 使其在相应空间中的范数的增长速度不快于指数型增长. 并用实例阐释了相关概念之间的关系. 借助于指数二分性的研究方法讨论了多项式二分性的特征, 所得结论推广了指数稳定性及指数二分性中的一些已有结果. 相似文献
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考虑n维散乱数据Hermit-Birkhoff型插值问题,在使给定的目标泛极小的条件下,构造了一种带自然边界条件的多元多项式样条函数插值方法.重点研究了插值问题解的特征,存在唯一性和构造方法,并讨论了收敛性及误差,最后给出了一些数值算例对方法进行验证. 相似文献
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We investigated an interpolation algorithm for computing outer inverses of a given polynomial matrix, based on the Leverrier–Faddeev method. This algorithm is a continuation of the finite algorithm for computing generalized inverses of a given polynomial matrix, introduced in [11]. Also, a method for estimating the degrees of polynomial matrices arising from the Leverrier–Faddeev algorithm is given as the improvement of the interpolation algorithm. Based on similar idea, we introduced methods for computing rank and index of polynomial matrix. All algorithms are implemented in the symbolic programming language MATHEMATICA , and tested on several different classes of test examples. 相似文献
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We present a fast algorithm based on polynomial interpolation to approximate matrices arising from the discretization of second-kind integral equations where the kernel function is either smooth, non-oscillatory and possessing only a finite number of singularities or a product of such function with a highly oscillatory coefficient function. Contrast to wavelet-like approximations, ourapproximation matrix is not sparse. However, the approximation can be construced in O(n) operations and requires O(n) storage, where n is the number of quadrature points used in the discretization. Moreover, the matrix-vector multiplication cost is of order O(nlogn). Thus our scheme is well suitable for conjugate gradient type methods. Our numerical results indicate that the algorithm is very accurate and stable for high degree polynomial interpolation. 相似文献
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本文利用多项式插值 ,对微分学和积分学中的一些典型题目 ,给出了统一的处理方法 .这种方法易于模仿 ,有一定的适用性 . 相似文献
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一类含三角形图的伴随多项式的根 总被引:1,自引:0,他引:1
YE Cheng-fu 《数学季刊》2004,19(3):280-285
We denote h(G,x) as the adjoint polynomial of graph G. In [5], Ma obtained the interpolation properties of the roots of adjoint polynomial of graphs containing triangles. By the properties, we prove the non-zero root of adjoint polynomial of Dn and Fn are single multiple. 相似文献
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F. Piazzon 《Applicable analysis》2013,92(5):1063-1073
We show that the property of being a (weakly) admissible mesh for multivariate polynomials is preserved by small perturbations on real and complex Markov compacts. Applications are given to smooth transformations of polynomial meshes and to polynomial interpolation. 相似文献
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It is known from the discrete harmonic analysis that the interpolation problem with equidistant interpolation points has a
unique solution. If the right-hand sides in the interpolation problem are fixed, the spline depends on two parameters: the
spline order and the number of points located between neighboring interpolation points. We find explicit expressions for the
limits of interpolation spllines with respect to each parameter separately and show that both repeated limits exist. We also
prove that these repeated limits are equal and their value is an interpolation trigonometric polynomial. Bibliography: 10
titles. Illustrations: 2 figures. 相似文献