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31.
修正了以第二类Chebyshev多项式的零点为插值结点组的拟Grünwald插值多项式,使之转化为积分形式,并利用不等式技巧和Hardy-Littlewood极大函数的方法,研究了此积分型拟Grünwald插值算子在带权Orlicz空间内的逼近问题,得出了意义相对广泛的逼近度估计的结果. 相似文献
32.
33.
Splines determined by the kernel of the differential operator are known to be useful to solve the singular boundary value problems of the form . One of the most successful methods is the collocation method based on special Chebyshev splines. We investigate the construction
of the associated B-splines based on knot-insertion algorithms for their evaluation, and their application in collocation
at generalized Gaussian points. Specially, we show how to obtain these points as eigenvalues of a symmetric tridiagonal matrix
of order k.
This research was supported by Grant 037-1193086-2771, by the Ministry of science, education and sports of the Republic of
Croatia. 相似文献
34.
高精度负荷预测在提高电力系统的安全性和经济性方面有着极其重要的意义,而现有的负荷预测方法因参数有限,难以完全反映其内在规律,因而导致预测结果不够准确.为此提出了一种基于Chebyshev多项式神经网络模型的预测方法.该方法使用递推最小二乘法训练神经网络权值系数,以获得高精度的参数估计,从而实现Chebyshev多项式神经网络模型对负荷量的最优拟合,再利用训练好的Chebyshev多项式神经网络模型实现中长期负荷预测.研究结果表明,该方法能较好模拟负荷变化规律,有效提高了负荷预测精度,在电力系统负荷预测中有较大的应用价值. 相似文献
35.
36.
A classical result on the expansion of an analytic function in a series of Jacobi polynomials is extended to a class of q-orthogonal polynomials containing the fundamental Askey–Wilson polynomials and their special cases. The function to be expanded
has to be analytic inside an ellipse in the complex plane with foci at ±1. Some examples of explicit expansions are discussed.
相似文献
37.
38.
This paper is devoted to the study of the approximation properties of linear operators which are partial Fourier--Legendre sums of order n with 2r terms of the form
k=1
2r
akPn+k(x) added; here P
m(x) denotes the Legendre polynomial. Due to this addition, the linear operators interpolate functions and their derivatives at the endpoints of the closed interval [-1,1], which, in fact, for r= = 1 allows us to significantly improve the approximation properties of partial Fourier--Legendre sums. It is proved that these operators realize order-best uniform algebraic approximation of the classes of functions
and A
q
(B). With the aim of the computational realization of these operators, we construct their discrete analogs by means of Chebyshev polynomials, orthogonal on a uniform grid, also possessing nice approximation properties. 相似文献
39.
G. Min 《Journal of Approximation Theory》1999,98(2):197
This note characterizes the denseness of rational systems
in C[−1, 1], where the nonreal poles in {ak}∞k=1
\[−1, 1] are paired by complex conjugation. This extends an Achiezer's result. 相似文献
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40.
A procedure for determining a few of the largest singular values and corresponding singular vectors of large sparse matrices is presented. Equivalent eigensystems are solved using a technique originally proposed by Golub and Kent based on the computation of modified moments. The asynchronicity in the computations of moments and eigenvalues makes this method attractive for parallel implementations on a network of workstations. Although no obvious relationship between modified moments and the corresponding eigenvectors is known to exist, a scheme to approximate both eigenvalues and eigenvectors (and subsequently singular values and singular vectors) has been produced. This scheme exploits both modified moments in conjunction with the Chebyshev semi-iterative method and deflation techniques to produce approximate eigenpairs of the equivalent sparse eigensystems. The performance of an ANSI-C implementation of this scheme on a network of UNIX workstations and a 256-processor Cray T3D is presented.This research was supported in part by the National Science Foundation under grant numbers NSF-ASC-92-03004 and NSF-ASC-94-11394. 相似文献