R_+~(n+1)上Carleson测度的特征

R_+~(n+1)上的正测度σ称为Carleson测度,如果存在常数N,对于R_+~(n+1)中底在R~n上边长为h的方体Q有 σ(Q)≤Nh~n. 本文研究Carleson测度的特征用BMO函数的积分性质来表达,主要结果如下: 若σ为R_+~(n+1)上的正测度,则σ为Carleson测度当且仅当存在只与n有关的常数K,对任意的f∈BMO(R~n)且Mf≠0,成立着这里,Mf表示f的Hardy-Little极大函数,u为f的Poisson积分,‖f‖_(?)为f的BMO(R~n)     

Fermat场址问题的信赖域算法

1 问题及预备引理 设R~n是n维欧氏空间，a_i∈R~n,i=1,2,…，t是t个不共线的点，w_i>0,i=1,2,…,t,┃·┃表欧氏范数，著名的Fermat场址问题是     

牛顿与二阶拟牛顿混合迭代方法

这里F:R~n→R~n是充分光滑的向量函数。用逐步迭代法求解(1.1)的主要方法有牛顿法或拟牛顿法。用二步或多步混合迭代方法求解(1.1),这种方法以前未曾见过。 1984年Pan提出二阶拟牛顿法,我们用1981年More,Garbow and Hillstrom提出的非线性方程组的测试函数对二阶拟牛顿方法进行测试,发现二阶拟牛顿法对于初始点及初始近似Jacobi阵的反应非常灵敏,若用牛顿法与二阶拟牛顿方法交替使用,其迭代过程所     

关于n维单形保多项式超限插值的表示问题

以R~n表示n维欧氏空间,Z_+~n是R~n中坐标均为非负整数的全体,e~s为Z_+~(n+1)中第s个坐标为1其余坐标为0的单位向量;π_d(R~n)为全次数不大于d的n元多项式全体,     

关于二元箱样条对偶基的进一步讨论

以R~n表示n维欧氏空间,Z~n表示其中分量皆为整数的点集.对α=(α_1,…,α_n)∈Z~n,称为α的长度.Z_+~n表示Z~n中各分量皆为非负整数的点集.若α∈Z_+~n,定义     

位势算子的带权向量值不等式

本文得到了某些积分算子的带权向量值不等式,这类算子是将 R~n 上函数映到 R_+~(n+1)上函数,利用这些结果,可得到 Poisson 积分的带权向量值不等式.     

关于“有首次积分的K型单调系统”一文的注记

1 引言及结果本文研究常微分方程系统x=F(x),x∈R_+~n,(1)这里F:R_+~n→R_+~n是C~1的.首先给出一些记号.令I={1,…,k},J={k+1,…,n}(0≤k≤n固定);K=R_+~k×(-R_+~(n-k)),R_+~n与K°分别为R_+~n与K的内部;x∈R~n,约定x_I={x_1…,x_k},类似定义x_J;x≤ky,当且仅当y-x∈K,x相似文献   

保欧氏度量偏序的变换

设L(R~n)表示n维欧氏空间R~n的所有线性变换构成的集合,‖ξ‖表示向量ξ的欧氏长度,由欧氏长度建立起向量间的序关系,令:PO(R~n)={f∈L(R~n)■|ξ,η∈R~(n×1),‖ξ‖≤‖η‖■‖f(ξ)‖≤‖f(η)‖}则PO(R~n)是欧氏空间R~n中保欧氏度量偏序变换构成的集合,讨论了PO(R~n)的结构,证明了保持这种序关系的变换由正交变换和伸缩变换组成.     

锥模型拟牛顿法

1 引 言 对于求解无约束最优化问题 min f(x),f:R~n→R,f∈C~2。Davidon提出了一类非二次模型方法,即锥函数近似模型 f(x)≈c(x)=f(x_k)+(f(x_k)~T(x-x_k))/((1-h_k~T(x-x_k))+1/2((x-x_k)~TA_k(x-x_k))/([1-h_k~T(x-x_k)]~2) (1.1)和共线调比变换     

无约束最优化的一个修正的类BFGS算法

利用前一步得到的曲率信息代替xk到xk+1段二次模型的曲率给出一个具有和BFGS类似的收敛性质的类BFGS算法,并揭示新算法与自调比拟牛顿法的关系.从试验函数库CUTE中选择标准试验函数,对比标准BFGS算法及其它改进BFGS算法进行数值试验.试验结果表明这个新算法的表现有点象自调比拟牛顿算法.     

Some Properties of Methods of Centers

Huard's method of centers is a method that solves constrained convex problems by means of unconstrained problems. In this paper we give some properties of this method, we analyse its convergence and rate of convergence and suggest some other variants and techniques to improve the speed of convergence.     

伪Newton—B族的导出及其性质

本文对无约束优化问题提出了一类新的近似牛顿法（伪牛顿-B族）,此方法同样具有二次终止性,产生的矩阵序列保持正定对称传递性。并证明了算法的全局收敛性和超级性收敛性。     

Convergence of the Tamed Euler Method for Stochastic Differential Equations with Piecewise Continuous Arguments Under Non-global Lipschitz Continuous Coefficients

In this paper, we deal with the strong convergence of numerical methods for stochastic differential equations with piecewise continuous arguments (SEPCAs) with at most polynomially growing drift coefficients and global Lipschitz continuous diffusion coefficients. An explicit and time-saving tamed Euler method is used to solve this type of SEPCAs. We show that the tamed Euler method is bounded in pth moment. And then the convergence of the tamed Euler method is proved. Moreover, the convergence order is one-half. Several numerical simulations are shown to verify the convergence of this method.     

Convergence Analysis of the Inexact Infeasible Interior-Point Method for Linear Optimization

We present the convergence analysis of the inexact infeasible path-following (IIPF) interior-point algorithm. In this algorithm, the preconditioned conjugate gradient method is used to solve the reduced KKT system (the augmented system). The augmented system is preconditioned by using a block triangular matrix. The KKT system is solved approximately. Therefore, it becomes necessary to study the convergence of the interior-point method for this specific inexact case. We present the convergence analysis of the inexact infeasible path-following (IIPF) algorithm, prove the global convergence of this method and provide complexity analysis. Communicated by Y. Zhang.     

Inexact-Newton method for solving operator equations in infinite-dimensional spaces

In this paper, we develop an inexact-Newton method for solving nonsmooth operator equations in infinite-dimensional spaces. The linear convergence and superlinear convergence of inexact-Newton method under some conditions are shown. Then, we characterize the order of convergence in terms of the rate of convergence of the relative residuals. The present inexact-Newton method could be viewed as the extensions of previous ones with same convergent results in finite-dimensional spaces.     

关于Brown方法的半局部收敛性

在本文中,我们讨论解非线性方程组的Brown方法的半局部收敛性。通过对Brown方法的算法结构作深入的分析,我们将Brown方法变换成带有特殊误差项的近似Newton法,基于这种等价变形,我们建立了Brown方法的半局部收敛定理,从而完善了Brown方法的收敛理论。     

Convergence analysis of waveform relaxation methods for neutral differential-functional systems

In this paper, the problems of convergence and superlinear convergence of continuous-time waveform relaxation method applied to Volterra type systems of neutral functional-differential equations are discussed. Under a Lipschitz condition with time- and delay-dependent right-hand side imposed on the so-called splitting function, more suitable conditions about convergence and superlinear convergence of continuous-time WR method are obtained. We also investigate the initial interval acceleration strategy for the practical implementation of the continuous-time waveform relaxation method, i.e., discrete-time waveform relaxation method. It is shown by numerical results that this strategy is efficacious and has the essential acceleration effect for the whole computation process.     

A study on the convergence of homotopy analysis method

In this study, a reliable approach for convergence of the homotopy analysis method when applied to nonlinear problems is discussed. First, we present an alternative framework of the method which can be used simply and effectively to handle nonlinear problems. Then, mainly, we address the sufficient condition for convergence of the method. The convergence analysis is reliable enough to estimate the maximum absolute truncated error of the homotopy series solution. The analysis is illustrated by investigating the convergence results for some nonlinear differential equations. The study highlights the power of the method.     

On an Inverse Free Steffensen-Type Method for the Approximation of Stiff Differential Equations

In this article, an inverse free Steffensen-type method is introduced. The method is applied to approximate the systems of equations associated to implicit schemes approximating a stiff differential equation. The method has quadratic convergence without evaluating neither any derivative nor inverse operator. Finally, hypotheses ensuring the semilocal convergence and the R-order of convergence are presented.     

On the global convergence of Chebyshev's iterative method

In [A. Melman, Geometry and convergence of Euler's and Halley's methods, SIAM Rev. 39(4) (1997) 728–735] the geometry and global convergence of Euler's and Halley's methods was studied. Now we complete Melman's paper by considering other classical third-order method: Chebyshev's method. By using the geometric interpretation of this method a global convergence theorem is performed. A comparison of the different hypothesis of convergence is also presented.