Error estimates for Hermite interpolation on spheres

In this paper, we prove convergence rates for spherical spline Hermite interpolation on the sphere S^d−1 via an error estimate given in a technical report by Luo and Levesley. The functionals in the Hermite interpolation are either point evaluations of pseudodifferential operators or rotational differential operators, the desirable feature of these operators being that they map polynomials to polynomials. Convergence rates for certain derivatives are given in terms of maximum point separation.     

Convergence of consistent and inconsistent finite difference schemes and an acceleration technique

This paper states and generalizes in part some recent results on finite difference methods for Dirichlet problems in a bounded domain Ω which the author has obtained by himself or with coworkers. After stating a superconvergence property of finite difference solution for the case where the exact solution u belongs to , it is remarked that such a property does not hold in general if . Next, a convergence theorem is given for inconsistent schemes under some assumptions. Furthermore, it is shown that the accuracy of the approximate solution can be improved by a coordinate transformation. Numerical examples are also given.     

线性约束多目标规划的非单调信赖域算法

本文对线性约束多规划问题提出了一类非单调信赖域算法 ,该方法是可行点法与信赖域技巧的结合 .在一定的条件下证明了算法的全局收敛性 .并进行了数值试验 .     

初始点任意的解非线性不等式约束优化问题的结合共轭梯度参数的超记忆梯度广义投影算法

本文利用广义投影矩阵,对求解无约束规划的超记忆梯度算法中的参数给出一种新的取值范围以保证得到目标函数的超记忆梯度广义投影下降方向,并与处理任意初始点的方法技巧结合建立求解非线性不等式约束优化问题的一个初始点任意的超记忆梯度广义投影算法,在较弱条件下证明了算法的收敛性．同时给出结合FR,PR,HS共轭梯度参数的超记忆梯度广义投影算法,从而将经典的共轭梯度法推广用于求解约束规划问题．数值例子表明算法是有效的．     

连续型单参指数族参数的经验Bayes检验问题:NA样本情形

本文对连续型单参指数族单边和双边假设检验问题导出了Bayes检验函数 ,利用同分布NA样本构造了经验Bayes(EB)检验函数 ,在适当条件下证明了EB检验函数的渐近最优性并获得了其收敛速度 ,文末给出一个满足定理条件的例子     

求解非线性P_0互补问题的非单调磨光算法

提出了一种新的磨光函数,在分析它与已有磨光函数不同特性的基础上,研究了将它用于求解非线性P_0互补问题时,其磨光路径的存在性和连续性,进而设计了求解一类非线性P_0互补问题的非单调磨光算法.在适当的假设条件下,证明了该算法的全局收敛性和局部超线性收敛性.数值算例验证了算法的有效性.     

The Topological Structure of Subseries Convergence

Let E be an abstract set, G be an Abelian topological group, FEG and be afamily of subsets of F. Let the sequence {xj}E be subseries aF convergent. In this paper,we present a sufficient and necessary condition for {xj} to be also subseries convergent in thetopology of uniform convergence on the sets in ,     

On the Glivenko-Cantelli problem in stochastic programming: Mixed-integer linear recourse

Expected recourse functions in linear two-stage stochastic programs with mixed-integer second stage are approximated by estimating the underlying probability distribution via empirical measures. Under mild conditions, almost sure uniform convergence of the empirical means to the original expected recourse function is established.     

解变分不等式的一种二次投影算法

该文研究一种新的解变分不等式的二次投影算法.通过构造一类新的严格分离当前迭代和变分不等式解集的超平面,进而建立了解决伪单调变分不等式投影算法的一种新的框架.通过改进已有结果的证明方法,证明了该算法生成的无穷序列是全局收敛的,并且在局部误差和Lipschitz条件下给出了收敛率分析.     

Implicit QR algorithms for palindromic and even eigenvalue problems

In the spirit of the Hamiltonian QR algorithm and other bidirectional chasing algorithms, a structure-preserving variant of the implicit QR algorithm for palindromic eigenvalue problems is proposed. This new palindromic QR algorithm is strongly backward stable and requires less operations than the standard QZ algorithm, but is restricted to matrix classes where a preliminary reduction to structured Hessenberg form can be performed. By an extension of the implicit Q theorem, the palindromic QR algorithm is shown to be equivalent to a previously developed explicit version. Also, the classical convergence theory for the QR algorithm can be extended to prove local quadratic convergence. We briefly demonstrate how even eigenvalue problems can be addressed by similar techniques. D. S. Watkins partly supported by Deutsche Forschungsgemeinschaft through Matheon, the DFG Research Center Mathematics for key technologies in Berlin.