ON THE RATE OF CONVERGENCE OF SOLUTIONS FOR A CLASS OF DIFFERENCE EQUATIONS

1IntroductionConsiderthefollowingdifferenceequationwhereGfRxR-Riscontinuous,p:Z -R ,k;Z -Z ,p(n)5M,k(n)5k,MER ,kEZ ;ZandZ denotethesetsofintegersandnonnegativeintegers,respective1y.Forintegersaand5,a>6,wedefineZ(a,5)={a,a l,'',6},Z(a)={a,a l,'.}.Weassumethat(i)G(x,.)ismonotonenon-decreasing,(ii)G(.,y)ismonotonenon-increasing;(iii)G(x,x)=o,G(x,y)5oforx>yandG(x,y)2oforx相似文献   

TRUNCATED HERMITE INTERPOLATION ON AN ARBITRARY SYSTEM OF NODES

1 IntroductionThis paper deals with the uniform collvergence of truncated Hermte illterpolatioll oll anarbitrary systelll of 11odes. Tl1e mean collvergellce of trllllcated Herntite interpolation oll a11arbitrary syste12l of 1lodes 1las been st11died recently by tlle al1t11or[31. The converge11ce oftruncated Hern1ite illterpolatiou on tl1e zeros of the Jacobi polynontials is discussed in both tlleweigl1ted LP and the unfform norm by P. Vertesi and Y. X.[61.First we iutroduce some defi11itio…     

Fluid approximation and its convergence Rate for GI/G/1 queue with vacations

A GI/G/1 queue with vacations is considered in this paper.We develop an approximating technique on max function of independent and identically distributed(i.i.d.) random variables,that is max{ηi,1 ≤ i ≤ n}.The approximating technique is used to obtain the fluid approximation for the queue length,workload and busy time processes.Furthermore,under uniform topology,if the scaled arrival process and the scaled service process converge to the corresponding fluid processes with an exponential rate,we prove by the...     

B-值随机变量序列大数定律的收敛速度

设{X_n:n≥1}是在某可分Banach空间B上取值的独立随机变量序列,S_n=X_1+…+X_n,n≥1,对某00和>1,定义P_n(ε)=P(‖S_n‖/n~(1/p)≥ε)。本文的目的是研究当n→+∞时,P(ε)→0的速度,在Banach空间上推广了Heyde和Rohatgi的结果;同时,本文还讨论了P_n(ε)→0的速度与S_n/n~(1/p)→0 a.s.的关系问题。     

ASYMPTOTIC PROPERTIES OF THE MOMENT CONVERGENCE FOR NA SEQUENCES

It is well-known that the complete convergence theorem for i.i.d. random variables has been an active topic since the famous work done by Hsu and Robbins [6]. Chow [4]obtained a moment version of Hsu and Robbins series. However, the series tends to infinity whenever ∈ goes to zero, so it is of interest to investigate the asymptotic behavior of the series as ∈ goes to zero. This note gives some limit theorems of the series generated by moments for NA random variables.     

具双时滞的SEIRS传染病模型指数收敛性

本文研究了一类具指数人口统计与结构的SEIRS传染病模型,利用一种新的基于比较原理的分析,获得了无病平衡点局部和全局指数稳定的两个充分条件.     

遗传算法的收敛速度估计

Under some conditions, the convergence of the genetic algorithms is investigated, corresponding convergence rates are estimated, and some related verifications are given in this paper.     

TRUNCATED HERMITE INTERPOLATION ON AN ARBITRARY SYSTEM OF NODES 1

The criteria of convergence, including a theorem of Grűnwald-type, and the rate of convergence in terms of the modulus ω_φ(f, t) of Ditzian and Totik for truncated Hermite interpolation on an arbitrary system of nodes are given.     

REGULARIZATION METHOD FOR IMPROVING OPTIMAL CONVERGENCE RATE OF THE REGULARIZED SOLUTION OF ILL-POSED PROBLEMS

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CONVERGENCE OF DERIVATIVES OF GENERALIZED BERNSTEIN OPERATORS

In the present paper, we obtain estimations of convergence rate derivatives of the q-Bernstein polynomials Bn (f, qn ; x) approximating to f ′ (x) asn →∞, which is a generalization of that relating the classical case qn = 1. On the other hand, we study the convergence properties of derivatives of the limit q-Bernstein operators B ∞ (f, q; x) as q → 1- .     

同时求解f(x)零点的一种迭代解法

1　引　　言在许多实际问题中 ,常常会遇到求解非线性方程 f( x) =0的根 ,或称为求函数 f( x)的零点 .此时 f( x) =( x-α) μg( x) ,且 g(α)≠ 0 ,μ为大于零的常数 ,称为零点α的根指数 .当 f( x)为 n次多项式 ,设 δ(l)k =-f( z(l)k ) /f′( z(l)k ) ,牛顿修正量迭代解法为z(l+1 )k =z(l)k +δ(l)k /( 1 +δ(l)k ni=1 ,i≠ k1z(l)k -z(l)i) ,　　 k =1 ,2 ,… ,n,　 l =0 ,1 ,2 ,… ( 1 )当所有根为单根时 ,迭代法收敛 ,且收敛阶为 3阶 (见 [1 ] ,[2 ] ,[3 ] ,[4 ] ) .当 f ( x)为 n次多项式 ,所有互不相同的根为 r1 ,r2 ,… ,rm,对应…     

OPTIMAL GLOBAL RATES OF CONVERGENCE OF M－ESTIMATES FOR MULTIVARIATE NONPARAMETRIC REGRESSION

ＯＰＴＩＭＡＬＧＬＯＢＡＬＲＡＴＥＳＯＦＣＯＮＶＥＲＧＥＮＣＥＯＦＭ－ＥＳＴＩＭＡＴＥＳＦＯＲＭＵＬＴＩＶＡＲＩＡＴＥＮＯＮＰＡＲＡＭＥＴＲＩＣ　ＲＥＧＲＥＳＳＩＯＮＳＨＩＰＥＩＤＥ（施沛德）（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ｔｈ...     

最优基选择变尺度变换方法收敛性分析

This paper deals with a nonparametric algorithm,named Affine Scaling Transformation (AST),for best basis selection.The characteristic nature of the algorithm provides a global convergence for sparse so...     

近似已知函数求导方法的改进

本文研究了近似已知函数求导方法的改进.利用Lagrange乘数法对罗方法中的系数进行了优化,得到了更快的收敛速度,并给出了相关的数值试验.     

同时具有点和区间半径序列收敛性的免导迭代法的进一步讨论

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     

分数Stratonovich随机积分的收敛速度

本文研究了分数布朗运动的随机积分的收敛性.利用卷积逼近的方法,我们得到了相应的收敛速度.     

On the Fine and Rough Theory of Lagrange Type Interpolation of Higher Order

Convergence of a general Gaussian quadrature formula is shown and its rate of convergence is also given.     

Mean Convergence of Lagrnage Type Interpolation on an Arbitrary System of Nodes

Abstract   Sufficient conditions of convergence and rate of convergence for Lagrange type interpolation in the weighted L ^p norm on an arbitrary system of nodes are given. Supported by the National Natural Sciences Foundation of China (No.19671082)     

Mean Convergence of Lagrange Type Interpolation on an Arbitrary System of Nodes

Abstract Sufficient conditions of convergence and rate of convergence for Lagrange type interpolation in theWeighted L~p norm on an arbitrary system of nodes are given.