圆盘定理的改进与弱连对角占优矩阵

本文对圆盘定理进行了改进，给出了特征值分布新的估计，由此引出了弱连对角占优矩阵，讨论了其基本性质，重点分析了该类矩阵的逆与分裂特征，证明了在该类矩阵条件下Ｈ－相容分裂是收敛分裂，并给出迭代矩阵谱半径的上界及ＳＯＲ算法中参数ω的选取范围。     

Polynomiality of primal-dual affine scaling algorithms for nonlinear complementarity problems

This paper provides an analysis of the polynomiality of primal-dual interior point algorithms for nonlinear complementarity problems using a wide neighborhood. A condition for the smoothness of the mapping is used, which is related to Zhu’s scaled Lipschitz condition, but is also applicable to mappings that are not monotone. We show that a family of primal-dual affine scaling algorithms generates an approximate solution (given a precision ε) of the nonlinear complementarity problem in a finite number of iterations whose order is a polynomial ofn, ln(1/ε) and a condition number. If the mapping is linear then the results in this paper coincide with the ones in Jansen et al., SIAM Journal on Optimization 7 (1997) 126–140. Research supported in part by Grant-in-Aids for Encouragement of Young Scientists (06750066) from the Ministry of Education, Science and Culture, Japan. Research supported by Dutch Organization for Scientific Research (NWO), grant 611-304-028     

随机环境中迁入分枝过程的极限性质

在方差和均值有限的条件下,得到了随机环境中迁入分枝过程对应的规范化过程的几乎处处收敛性和L^2收敛性．这对于刻画过程本身的发散速度,具有重要的意义．     

Averaging of Backward Stochastic Differential Equations and Homogenization of Partial Differential Equations with Periodic Coefficients

Abstract

We study the limit of the solutions of systems of semi-linear partial differential equations (PDEs) of second order of parabolic type, with rapidly oscillating periodic coefficients, a singular drift, and singular coefficients of the zero and second order terms. Our basic tool is the approach given by Pardoux [14 Pardoux , E. 1999 . Homogenization of linear and semilinear second order parabolic PDEs with periodic coefficients: a probabilistic approach . J. Funct. Anal. 167 : 498 – 520 . [CSA] [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar]]. In particular, we use the weak convergence of an associated backward stochastic differential equation (BSDE).     

求解非线性方程根四阶收敛的迭代格式

提出了求解非线性方程根新的四阶收敛迭代方法,新方法每次迭代只需要两次函数计算,一次一阶导数值计算,效能指数达到1.587.通过几个数值算例来解释该方法的有效性.     

扰动压缩条件的点列收敛性问题

研究完备度量空间X中满足ρ(xn,xn+1)≤Lρ(xn-1,xn)+εn的点列{xn}收敛性问题,其中L∈(0,1)为常数,εn非负是无穷小量称为扰动.文中的主要结论是:点列{xn}的收敛性由扰动εn决定,即当幂级数sum from n=1 to ∞εnxn的收敛半径R>1/L时,点列{xn}收敛.特别地,当R>1时,点列收敛;而R=1时,{xn}敛散性不能确定.     

无线搜索下仿射尺度算法的收敛性

本文我们考虑求解边界约束优化问题的一个仿射尺度算法。该方法的主要特点是在每次迭代过程中不需要任何线搜索,从而避免了多次调用目标函数的计算。在一定条件下,获得了算法的全局收敛性,数值测试证明了方法的有效性。     

Navier–Stokes equations with nonhomogeneous boundary conditions in a convex bi-dimensional domain

We prove the existence of a weak solution to Navier–Stokes equations describing the isentropic flow of a gas in a convex and bounded region, ΩR², with nonhomogeneous Dirichlet boundary conditions on ∂Ω. These results are also extended to flow domain surrounding an obstacle.     

Convergence of numerical solutions for variable delay differential equations driven by Poisson random jump measure

We study the following stochastic differential delay equations driven by Poisson random jump measure

     

Explicit averaging cyclic algorithm for common fixed points of asymptotically strictly pseudocontractive maps

Weak and strong convergence theorems for the approximation of common fixed points of a finite family of asymptotically strictly pseudocontractive mappings are proved in Hilbert spaces using an explicit averaging cyclic algorithm.