CONVERGENCE OF THE WEIGHTED NONLOCAL LAPLACIAN ON RANDOM POINT CLOUD

We analyze the convergence of the weighted nonlocal Laplacian (WNLL) on the high dimensional randomly distributed point cloud.Our analysis reveals the importance of the scaling weight,μ ～ |P|/|S| with |P| and |S| being the number of entire and labeled data,respectively,in WNLL.The established result gives a theoretical foundation of the WNLL for high dimensional data interpolation.     

关于单调变分不等式的不精确邻近点算法的收敛性分析

We consider a proximal point algorithm(PPA) for solving monotone variational inequalities. PPA generates a sequence by solving a sequence of strongly monotone subproblems .However,solving the subproblems is either expensive or impossible. Some inexact proximal point algorithms(IPPA) have been developed in many literatures. In this paper, we present a criterion for approximately solving subproblems. It only needs one simple additional work on the basis of original algorithm, and the convergence criterion becomes milder. We show that this method converges globally under new criterion provided that the solution set of the problem is nonempty.     

求凸集公共点的行处理方法的收敛性证明

行处理方法(Row-Action)是数值代数与数值优化的一大类方法,这方面已有许多研究,并且已有综述性评论,本文对下面问题有兴趣:问题 A.给定 R~n 中一族闭凸集{Q_i}_i~m=1,且 S=(?)Q_i≠φ,求 x∈S.显然解线性方程组及线性不等式组是问题 A 的特例.Gubin 等在1967年提出如下的行处理算法:     

线性过程的收敛速度

设X_t=sum from j=0 to ∞ c_jε_(t-j)是一个线性过程,当{ε_t}是一个局部广义高斯随机序列时,我们获得了X_t的重对数收敛速度。     

关于Ф-伪压缩型映象的具误差的Ishikawa和Mann迭代过程的收敛性问题

在Bannah空间中,研究了多值Ф-伪压缩型映象的具误差的Ishikawa和Mann迭代过程的收敛性问题.所得结果改进,发展和统一了许多人的最新结果.     

关于非线性不等式组Levenberg-Marquardt算法的收敛性(英文)

本文研究了一类非线性不等式组的求解问题.利用一列目标函数两次可微的参数优化问题来逼近非线性不等式组的解,光滑Levenberg-Marquardt方法来求解参数优化问题,在一些较弱的条件下证明了文中算法的全局收敛性,数值实例显示文中算法效果较好.     

信息熵的收敛性与收敛速度

本讨论了连续时间,状态空间有限的马氏过程的信息熵的收敛性质,给出了可测转移矩阵的极限形式,得出具有可测转移矩阵的马氏过程的信息熵在时间趋于无穷大时存在且有限,对于具有强遍历转移函数的马氏过程的信息熵按多项式一致收敛。     

关于一类具有大范围收敛性的迭代法

本文由Hadamard因子分解定理出发,证明了推广的Laguerre迭代方法对求解一类超越方程具有大范围收敛性.对复根允许存在的区域作了讨论.得出了Riemann假定成立的一个必要条件.还给出了此迭代法的Algol 60程序.     

关于伽略金方法收敛阶的估计

§1.引言设H是可分的Hilbert空间,内积为(·,·),范数为||·||.v是H的稠密子空间.于V定义另一内积[·,·]和相应的范数|·|,使v关于[·,·]具有Hilbert空间结构。假定v往H的嵌入:v|→H连续,即存在常数a>0,使 ||u||≤a|u|,uv. (1) 设L_1,L_2是由v到H的线性算子,其定义域D_(L_1),D_(L_2)是v的线性稠密子集,且D_(L_1)D_(L_2).令A=L_1+L_2(显然A的定义域D_A=D_(L_ I))。对H,我们考虑算子方程     

Smale点估计理论与Durand—Kerner程序的收敛性

全部单零点α_i(i=1,2,…,n)的有效算法。 关于(1.1)的存在、收敛问题,已有文献的立足点是基于Newton-Kantorovich定理。 Smale关于Newton法的点估计理论是别开生面的,他摆脱了Newton-Kantoro-vich定理中的区域性Lipschitz条件,利用映象的解析性质,取得了只依赖于初始点上的信息去确定Newton法的敛散行为的结论。但此条件并不实用,甚至比Kantorovich的     

ON THE CONVERGENCE OF GODUNOV SCHEME FOR NONLINEAR HYPERBOLIC SYSTEMS

51. IntroductionWe consider the one dimensional Cauchy problem for an n x n system of the formHere A(u) is a smooth matrix valued map from a domain U C R" into R", and (x, t) eR x R . The system is assumed to be strictly hyperbolic, i.e. the matrix A(u) has n realand strictly different eigenvalues at each point u C U.We note that even for smooth data a classical solution is only defined locally in time.In general the solution will develop discontinuities in finite time and it is not cle…     

关于补几何规划算法的收敛性

几何规划是非线性规划的一个分支. Zener,Duffin与Peterson最初以几何平均≤算术平均这一著名的不等式为基础发展了一套研究正项几何规划     

关于解极大相关问题P-SOR算法的收敛性

对求解极大相关问题的P-SOR方法的收敛性做了进一步研究.得到了一些新的收敛条件.为了提高收敛到全局最大解的可能性,提出了一种新的初始向量选择策略.给出了P-SOR算法的对称形式(P-SSOR).还给出了一种算法精化策略.最后,用数值例子说明新方法的有效性.     

ON THE CONVERGENCE OF IMPLICIT DIFFERENCE SCHEMES FOR HYPERBOLIC CONSERVATION LAWS

1. IntroductionWe are are interested in the fOllowing Cauchy problem for scalar conservation lawswhere the initial data uo E BV(R) and the flux function f 6 C'(n).It is well known that this problem may not always have a smooth global solution even ifthe i…     

ON THE CONVERGENCE OF AN APPROXIMATE PROXIMAL METHOD FOR DC FUNCTIONS

In this paper we prove the convergence of the approximate proximal method for DC functions proposed by Sun et al [6]. Our analysis also permits to treat the exact method. We then propose an interesting result in the case where the second component of the DC function is differentiable and provide some computational experiences which proved the efficiency of our method.     

关于解非线性方程组的King-Werner叠代过程的收敛性

解非线性方程组P(x)=0的Newton叠代法S_(n 1)=u(x_n)的种种改进与其叠代函数u(x)=x-P’(x)~(-1) P(x)由一目拓广到两目ω(x,z)=x-P’(z)~(-1)P(x)有关,King-Werner的改进方案x_(n 1)=w(x_n, 1/2(x_n y_n)),y_(n 1)=w(x_(n 1),1/2(x_n y_n))保持计值量不变而使收敛阶达到1 2~(1/2),我们证明了,设P:D? C~N→C~N在凸区域D上具有以L为常数的Lipschitz连续的二阶Frechet导数P″(x),||P″x||≤M x∈D,?x_0∈D,x_1=u(x_0),||x_1-x_0||≤η, ||P’(x_0)~(-1)||≤β,M 1/12Lη≤K,h=Kβη≤1/2,S≡{x|||x-x_1||≤η(1-(1-2h)~(1/2)/(1 (1-2h)~(1/2))}?D,则King-Werner叠代过程产生的x_n和y_n都属于S并且收敛于N元方程组P(x)=0的解,这个结论,与关于Newton叠代过程收敛性的Ostrowski-定理十分相似。     

ON THE CONVERGENCE OF PROJECTOR-SPLINES FOR THE NUMERICAL EVALUATION OF CERTAIN TWO-DIMENSIONAL CPV INTEGRALS

In this paper, product formulas based on projector-splines for the numerical evaluation of 2-D CPV integrals are proposed. Convergence results are proved, numerical examples and comparisons are given.     

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   

基于函数型数据的系数正则化回归的收敛速度

本文研究了基于函数型输入和₁-正则化的最小二乘回归问题的推广性能.利用基于Rademacher平均的分析技术,获得了学习速度的估计,推广了已有的欧式空间有限维输入结果.