共查询到20条相似文献,搜索用时 93 毫秒
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1 引 言 传统的求零点的迭代法只讨论迭代序列{xn}的收敛阶,近年来,G.Alefeld和F.A.Po-tra研究了含零点的区间半径序列的收敛性[2][3],而我们提出了同时具有点和区间半径序列均平方收敛的免导迭代法[1],即当n充分大时,序列{xn}和含零点区间的半径序列{(bn-an)}都是平方收敛的.通过进一步的分析,我们发现,文[1]中的结果仍可改进,并且,不需 相似文献
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潘壮元 《高等学校计算数学学报》1988,(2)
格式(1.1)每步只需求一次导算子的逆,计算量比现有的加速迭代格式均少,同时具有高阶收敛性。格式(1.2)与文[1]中提出的迭代格式相比,计算量基本相同,但其收敛速度却较快。我们在§2中给出算法(1.1)和(1.2)的收敛性定理及误差估计。对于高阶奇异问题,§3中也给出了相应的加速迭代格式和收敛性定理。§4中给出数值例子。 相似文献
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构造求根迭代公式的一种方法 总被引:2,自引:0,他引:2
本文给出了构造方程求根迭代公式的一种方法,条件简单,便于应用。所得公式具有大范围收敛性,初值可任取,能在任一有限区间上求出方程的全部实根,或判断出方程无实根的情况。将这种方法应用到不同的函数类上,就可得到各种不同的具体的迭代公式。例如,应用到二次连续可微函数类上,就包含了[2],[3]的结果;应用到连续函数类上,就包含了[4]的结果。本文还给出了另外的特例,包括不需要在每步迭代中计算一阶导数和二阶导数的特例,以及不用[1]—[4]中公式求解的特例。对收敛阶也进行了讨论。 相似文献
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1引言有限元导数恢复技术是近年来发展起来的计算有限元导数并获得导数逼近超收敛性的一种新的后处理技术.对于一维和二维区域上的二阶椭圆边值问题,文[1,2]提出了Z-Z小片插值技术,得到了有限元导数逼近在小片恢复区域上的一阶超收敛结果和剖分节点处二阶强超收敛性;文[3,4]则建立了更为实用的小片插值恢复技术并得到与文[1,2]相平行的超收敛结果;文[5]对两点边值问题构造了一种积分形式的导数恢复公式,利用这个公式可获得剖分节点处有限元导数逼近的O(h~(2k))阶超收敛估计.本文将对一维四阶椭圆 相似文献
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<正> 用Jacobi 迭代法解线性方程组AX=b(其中A∈R~(n×n)、b∈R~n.X∈R~n)时,一般假定A 为可逆阵且a_(ii)≠0(i=1,2,…n)。文[1]指出.如果矩阵A 为严格对角占优阵,则Ja obi 迭代过程是收敛的。‘严格对角占优’这个条件是比较强的,它限制了Jacobi 迭代法的应用范围。实际 相似文献
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刘桂香 《高等学校计算数学学报》2006,28(1):33-38
1 引言和引理
文[1]中Ben-Israel与Greville给出了计算矩阵A的Moore-Penrose逆的一阶和p创迭代法,陈永林[2]推广了[1]的结果,给出了类似的计算矩阵A的具有指定值域T与零空间S的(2)-逆A^(2)T,S的一阶迭代法 相似文献
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Kunyang Wang Feng Dai 《分析论及其应用》2007,23(1):50-63
As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years (2001-2005). The main topics are: convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths. 相似文献
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Yuxian Zheng 《分析论及其应用》2006,22(2):136-140
In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p(R^n) into the Lebesgue space L^p with p 〈 1. 相似文献
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H. H. Cuenya M.D. Lorenzo C. N. Rodriguez 《分析论及其应用》2007,23(2):162-170
In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms. 相似文献
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《中国科学 数学(英文版)》2014,(8)
<正>May 26,2014,Beijing Science is a human enterprise in the pursuit of knowledge.The scientific revolution that occurred in the 17th Century initiated the advances of modern science.The scientific knowledge system created by 相似文献
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《计算数学》2014,(2)
<正>August 10-14,2015Beijing,ChinaThe International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists 相似文献
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W.M.Shah A.Liman 《分析论及其应用》2004,20(1):16-27
Let P(z)=∑↓j=0↑n ajx^j be a polynomial of degree n. In this paper we prove a more general result which interalia improves upon the bounds of a class of polynomials. We also prove a result which includes some extensions and generalizations of Enestrǒm-Kakeya theorem. 相似文献
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In this paper, the authors study the boundedness of the operator [μΩ, b], the commutator generated by a function b ∈ Lipβ(Rn)(0 <β≤ 1) and the Marcinkiewicz integrals μΩ, on the classical Hardy spaces and the Herz-type Hardy spaces in the case Ω∈ Lipα(Sn-1)(0 <α≤ 1). 相似文献
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Francois Chaplais 《分析论及其应用》2006,22(4):301-318
In applications it is useful to compute the local average empirical statistics on u. A very simple relation exists when of a function f(u) of an input u from the local averages are given by a Haar approximation. The question is to know if it holds for higher order approximation methods. To do so, it is necessary to use approximate product operators defined over linear approximation spaces. These products are characterized by a Strang and Fix like condition. An explicit construction of these product operators is exhibited for piecewise polynomial functions, using Hermite interpolation. The averaging relation which holds for the Haar approximation is then recovered when the product is defined by a two point Hermite interpolation. 相似文献
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A.Al-Shuaibi F.Al-Rawjih 《分析论及其应用》2004,20(1):28-34
Given the Laplace transform F(s) of a function f(t), we develop a new algorithm to find an approximation to f(t) by the use of the classical Jacobi polynomials. The main contribution of our work is the development of a new and very effective method to determine the coefficients in the finite series expansion that approximation f(t) in terms of Jacobi polynomials. Some numerical examples are illustrated. 相似文献