求解约束极小极大问题的一种K─S函数的近似迭代法

借助于极大熵方法和逼近法，给出了一种求解约束极小极大问题的K－S函数近似迭代法，同时讨论算法的有关收敛性．     

并行计算的带有高阶导数的块隐式单步法

本文讨论了一类并行计算常微分方程初值问题的带有高阶导数项的块隐式单步方法,这种方法可以在 K 台处理机上并行进行数值处理.本文对方法的一般性质及方法收敛的条件进行了讨沦,得到方法的阶数为2l,并且指出适 l≤4时方法是 A-稳定的,最后给出了一个数值例子.     

一类亚半正定矩阵的左右逆特征值问题

1．引言在工程技术中常常遇到这样一类逆特征值问题：要求在一个矩阵集合S中，找具有给定的部分右特征对（特征值及相应的特征向量）和给定的部分左特征对（特征值及相应的特征向量）的矩阵．文［2］，［3］讨论了S为。x。实矩阵集合的情形．文［4］－［7］对S为nxn实对称矩阵．对称正定矩阵，对称半正定矩阵集合的情形进行了讨论．文【川讨论了S为亚正定阵集合的情形．并提到了对于亚半正定矩阵的情形目下无人涉及，有待进一步研究．本文将对S为nxn亚半正定矩阵集合的情形进行讨论．给出了亚半正定矩阵的左右逆特征值问题有解的充要条件…     

具有高阶导数的块隐式混合单步并行计算方法

该文讨论了一类求解常微分方程初值问题的具有高阶导数项的块隐式混合单步并行计算方法．这种算法的块数为k，价数为（l十1）（d＋1），可以在s台处理机上进行并行计算，其中l是高阶导数的阶数，k＝s·d.该文讨论了方法的一般性质及数值稳定性，最后给数值例子。     

关于随机差分方程的一个注记及其在GARCH模型中的应用

本文对Kesten(1973)中的关_十随机矩阵的更新理论作了一个注记，给出了一个计算尾部指数K1的一个简易方法，并利用此讨论了ARCH(2)和GARCH(2，1)两个时间序列模型的平稳域和分布尾部概率，同时给出一些直观的数值结果。本文结果可看作是对Embrechts et al．(1997)和Mikosch及starica(2000)关于一维随机差分方程应用结果的一个推广．     

布尔函数Walsh变换的非零取值个数

设Wf(y)(y∈F2^r)是布尔函数f：F2^r→F2的Walsh变换．Sf为Wf(y)≠0的y个数，S为所有Sf的并集(其中f过所有可能的布尔函数)．决定集合S是通信和信息安全领域一个重要问题．本文利用群环工具给出研究这一问题的新方法．用这种方法以统一方式证明了[4]中的结果．并利用群环方法给出了关于集合S的一系列新结果．     

块θ-方法的PL-稳定性

1．引言在［6］中作者介绍了所谓块0一方法求解初值问题：这个方法具有精度高，数值稳定性好等优点，并证明了它是A-稳定的充分必要条件为051．本文将给出数值方法求解滞后微分方程时的PL一稳定性的概念，然后给出块0一方法为PL一稳定的充分必要条件．我们沿用［61中的记号介绍块0一方法及它的一些基本性质．所谓H一维块0一方法是使用已知k个点上的函数值求出后面k个点上的值．令其中O／L＼＿如果知道最初的yo，yi，…，yk－1，便能由（1．2）式设法求出yk，yk＋1；…，yZk－1，如此继续．下面两个定理是块令方法的基本性质．定理1．1［…     

Banach空间中的渐近赋范性质

本文讨论了Banach空间中的一些渐近赋范性质K，给出了Banach空间中一些特殊空间及其它们之间的关系，并特别讨论了1-ANP-K关于KP，KKP，GP性质．     

定数截尾恒定应力加速寿命试验的最优设计

本文讨论了在指数分布下K个应力情况满足条件（3．3）的恒加试验，并给出它的最优设计。     

由三角形投影问题再探椭圆面积

椭圆面积公式S=πab，其中π为圆周率，α、b分别是椭圆半短轴、半长轴的长．关于椭圆面积公式的证法有多种，文献[1]利用仿射变换与仿射不变量推导出椭圆面积公式，文献[2]通过对单位正方形的拉伸（压缩）变换前后面积关系的讨论，给出了椭圆面积公式的又一证法．文献[3]利用初等数学的方法，推导出椭圆面积的计算公式．本文利用投...     

Local search in problems with nonconvex constraints

Nonconvex optimization problems with an inequality constraint given by the difference of two convex functions (by a d.c. function) are considered. Two methods for finding local solutions to this problem are proposed that combine the solution of partially linearized problems and descent to a level surface of the d.c. function. The convergence of the methods is analyzed, and stopping criterions are proposed. The methods are compared by testing them in a numerical experiment.     

Low‐order,P‐stable,two‐step methods for use with lax accuracies

A semi‐implicit family of two‐step methods is considered for the numerical solution of . These methods are hybrid and waste two stages (function evaluations) per step in order to attain fourth algebraic order while other methods of this type need three stages per step. Exploiting this improvement, we derive a particular method and conclude with a series of numerical tests on stiff periodic problems that illustrate its efficiency.     

人工压缩方程的OBLC区域分解法

本文根据物理尺度的区域分解法[1],[2],从奇异摄动的观点把解分为外部解和边界层校正,两者在固定的物面边界上藕合,这样对不同的尺度区域,可用不同的简化方程及计算方法.本文给出了人工压缩N-S方程的特征性质及其合适的边界提法,计算的例子表明,精度和效率是满意的.     

A nested dissection approach for sparse matrix partitioning

We consider how to partition and distribute sparse matrices among processors to reduce communication cost in sparse matrix computations, in particular, sparse matrix-vector multiplication. We consider 2d distributions, where the distribution is not constrained to just rows or columns. We present a new model and an algorithm based on vertex separators and nested dissection. Preliminary numerical results for sparse matrices from real applications indicate the new method performs consistently better than traditional 1d partitioning and is often also better than current 2d methods. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Element-based index reduction in electrical circuit simulation

The numerical simulation of very large scale integrated circuits is an important tool in the development of new industrial circuits. In the course of the last years, this topic has received increasing attention. Common modeling approaches for circuits lead to differential-algebraic systems (DAEs). In circuit simulation, these DAEs are known to have index 2, given some topological properties of the network. This higher index leads to several undesirable effects in the numerical solution of the DAEs. Recent approaches try to lower the index of DAEs to improve the numerical behaviour. These methods usually involve costly algebraic transformations of the equations. Especially, for large scale circuit equations, these transformations become too costly to be efficient. We will present methods that change the topology of the network itself, while replacing certain elements in oder to obtain a network that leads to a DAE of index 1, while not altering the analytical solution of the DAE. This procedure can be performed prior to the actual numerical simulation. The decreasing of the index usually leads to significantly improved numerical behaviour. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Subgradient Method for Nonconvex Nonsmooth Optimization

In this paper, we introduce a new method for solving nonconvex nonsmooth optimization problems. It uses quasisecants, which are subgradients computed in some neighborhood of a point. The proposed method contains simple procedures for finding descent directions and for solving line search subproblems. The convergence of the method is studied and preliminary results of numerical experiments are presented. The comparison of the proposed method with the subgradient and the proximal bundle methods is demonstrated using results of numerical experiments.     

On the Whitham system for the (2+1)-dimensional nonlinear Schrödinger equation

Whitham modulation equations are derived for the nonlinear Schrödinger equation in the plane ((2+1)-dimensional nonlinear Schrödinger [2d NLS]) with small dispersion. The modulation equations are obtained in terms of both physical and Riemann-type variables; the latter yields equations of hydrodynamic type. The complete 2d NLS Whitham system consists of six dynamical equations in evolutionary form and two constraints. As an application, we determine the linear stability of one-dimensional traveling waves. In both the elliptic and hyperbolic cases, the traveling waves are found to be unstable. This result is consistent with previous investigations of stability by other methods and is supported by direct numerical calculations.     

广义K.d.V.方程的数值方法

本文研究一般的广义K.d.V.方程的数值方法,给出了广义K.d.V.方程的一类半离散差分格式,证明了它们的守恒性。作者还严格证明了这类格式的广义稳定性,并由此推出收敛性。文章的最后考虑了全离散情形和两步格式。     

基于PDE和几何曲率流驱动扩散的图像分析与处理

本文介绍由变分优化模型导出的偏微分方程(PDEs)模型与几何曲率流驱动扩散在图像恢复方面的应用，以及多种非线性异质扩散模型，讨论了PDEs模型在图像分析与处理方面的优点，理论与实验结果表明，要恢复得到商质量的图像，PDEs模型的利用是极为必要的．文中还介绍了求解PDEs模型的数值方案．其中，曲率计算是一个关键问题，其结果直接参与自适应扩散的控制．详细总结了基于有限差分和水平集方法，求解藕合非线性异质扩散模型方程的数值方案，追求高质量图像、高精度计算方法、降低计算复杂性是本文处理方法不断进步的发展动力。     

Fast approximate computation of a time-harmonic scattered field using the on-surface radiation condition method

The numerical study of the on-surface radiation condition methodapplied to two- and three-dimensional time-harmonic scattering problems is examined. This approach allows us to quickly computean approximate solution to the initial exact boundary-valueproblem. A general background for the numerical treatment ofarbitrary convex-shaped objects is stated. New efficient on-surfaceradiation conditions leading in a natural way to a symmetricalboundary variational formulation are introduced. The approximationis based upon boundary finite-element methods. Moreover, thisstudy requires a specific numerical treatment of the curvatureoperator. To this end, a numerical procedure using some resultsabout the theory of local approximation of surfaces is described.Finally, the effectiveness and generality of the approach isnumerically tested for several scatterers.