关于L~1空间中Fredholm积分方程数值解的误差估计

将Fredholm积分方程的算法推广到更一般的情形,且证明其收敛性,并给出这种更精确算法的误差估计.数值算例进一步验证了算法的合理性.     

精细辛几何算法的误差估计

该文讨论了精细辛几何算法的计算误差,先展开二阶和四阶精细辛几何算法的表达式得到误差同精细剖分数目的关系,然后分析了任意阶精细辛几何算法的误差,得到了一致简洁的结果,总的误差可近似表示为单个精细步长的误差乘以剖分数目,最后讨论了在要求控制精度下剖分数目的选取,该方法克服了算法精度对积分时间步长的依赖性.     

利用蒙特卡罗方法求解数值积分

本文介绍了蒙特卡罗方法的主要思想和理论基础，以一维定积分与二维定积分为例，应用蒙特卡罗方法借助R语言模拟计算定积分的值，并给出结果的相对误差与样本量的关系.     

解带有Hilbert核的奇异积分方程的高精度组合算法

该文给出了用求积法解带Hilber核的奇异积分方程的高精度组合算法.把网格点分成互不相交的子集合, 在子集合上并行求解离散方程组, 再利用组合算法求得全局网格点的逼近.如果积分方程的系数属于B_δ, 则求积法的精度可达O(e^-nδ). 此外, 使用组合算法不仅能得到更高的精度阶, 而且能够得到后验误差估计. 数值算例的结果表明组合算法是极其有效的.     

无界弦自由振动问题的算法

探讨了无界弦自由振动问题的两种算法：行波法和积分变换法，主要就积分变换法利用富里叶变换和matlab软件使得计算更简单，并给出了积分变换法的一般算法．     

2.5维介质Born近似波速反演唯一性

考虑脉冲源引起的２．５维弱不均匀介质波速反演问题，利用线性化方法得到了波速的二维小扰动满足的积分方程，这是一个积分几何的问题，进而由Ｆｏｕｒｉｅｒ变换和脉冲函数的性质将此二维积分方程化为单变量的积分方程，最后用压缩映象理论证明了积分方程解的唯一性。本文给出了二给波速反演的一种新算法。同时，唯一性结果证明了已有的迭代算法的合理性。     

基于Hat函数的配置法解多维分数阶Fredholm积分方程

配置法是数值计算中常用的直接算法,具有数值稳定性好和计算精度高的优点.采用以hat函数为基底的配置法求解多维分数阶Fredholm积分方程.首先结合hat函数的性质,通过以hat函数为基底建立的配置法将分数阶积分方程转化为代数方程进行求解.然后在投影算子理论的框架下,建立了方程的收敛性理论并给出了误差分析.最后利用数值算例通过与其他数值方法相比较,验证了算法的高精度和高效率.     

地球物理正问题计算的小波方法

本将小波分析方法用于一类奇异积分方程的计算，建立了小波展开的非标准形式与标准形式转换关系，根据Mallat小波快速算法，设计了此类积分的计算算法，并通过实际例子验证了方法的有效性，计算具有速度快，运算量少的特点。     

双势理论用于处理非关联材料本构

基于传统塑性力学框架下的显式积分算法和基于Simo-Taylor提出的回退映射隐式积分算法是固体力学中两大经典本构积分算法.以经典的非关联材料模型Drucker-Prager(D-P)模型和Armstrong-Frederick(A-F)模型为例分别回顾了显式积分算法和隐式积分算法.以双势理论为基础,将双势的概念运用到材料的自由能中,将材料分为显式标准材料和隐式标准材料.两种传统积分算法都能有效地处理显式标准材料的本构关系,但在处理隐式标准材料时却存在一定的问题.双势积分算法是建立在双势理论下的本构积分算法,此算法不仅能够处理显式标准材料,对于处理隐式标准材料,也存在一定的优势.通过变分原理推导了双势积分算法解的存在性,运用双势积分算法处理Drucker-Prager模型和Armstrong-Frederick模型,并与经典传统积分算法得到的结果进行对比,验证了双势本构积分算法的稳定性和准确性.     

中心焦点判定的形式积分因子方法

本文从积分因子的角度探讨了焦点量的计算方法，给出了形式积分因子的存在性和形式积分因子的系数与焦点量的等价关系，从而给出计算焦点量的简捷算法。     

A multicast routing algorithm based on searching in directed graph

Aiming at constructing a delay and delay variation bounded Steiner tree in the real-time streaming media communication, in this paper, we discuss a multicast routing algorithm based on searching a directed graph (MRASDH). During the process of the construction of the multicast tree, some nodes and links in the network topology do not affect the outcome of the constructed tree. Therefore, based on the thought of shrinking the search space through deleting these non-relative nodes and edges to the utmost, the ant algorithm is utilized to generate a directed sub-graph of the network topology for each destination node, in which each node owns a bounded out-degree. And all these sub-graphs can be merged into a new directed graph that serves as the new search space. In the new space, the simulated annealing algorithm is applied to obtain a multicast tree that satisfies the condition for the optimization. The performance analysis and simulation results demonstrate that this algorithm can effectively construct a delay and delay variation bounded multicast tree. They also show that the algorithm have lower time complexity than the current ones, which means a much better result would be achieved when the system scale rises greatly.     

Speeding up the Floyd-Warshall algorithm for the cycled shortest path problem

On a network with a cycle, where at least one cycle exists, the Floyd-Warshall algorithm is one of the algorithms most used for determining the least cost path between every pair of nodes. In this work a new algorithm for this problem is developed that requires less computational effort than the Floyd-Warshall algorithm. Furthermore, we show that the basis of our algorithm is much easier to understand, which might be an advantage for educational purposes. A small example validates our algorithm and shows its implementation.     

交替方向的扩散方程精细积分并行算法

给出了交替方向的二维扩散方程的精细积分算法，将一个时间步积分分为两个方向，使大规模矩阵的计算转化为一些小矩阵的计算，减小了每一步求解的计算量．对于方形区域的齐次方程，计算结果与全城精细积分完全相同，而计算量和存储量都要小得多．算例表明了算法具有较高的并行计算加速比和计算效率．     

An improved GPS method with a new pseudo-peripheral nodes finder in finite element analysis

Finding pseudo-peripheral nodes with the largest eccentricity is important in matrix bandwidth and profile reduction algorithms in finite element analysis. A heuristic parameter, called the “width-depth ratio” and denoted by κ, is presented for finding the pseudo-peripheral nodes with larger pseudo-diameter compared with the GPS (Gibbs-Poole-Stockmeyer) pseudo-peripheral nodes finder. A novel nodes renumbering algorithm is thus developed by using our nodes finder based on GPS method. Simulations show that proposed nodes finder is reliable and effective in locating the proper pseudo-peripheral nodes with larger pseudo-diameters. A shielded microstrip line is given as an example to testify the ability of the proposed algorithm in application. The results, including time, pseudo-diameter, bandwidths and profiles, all indicate that our method is more competitive than GPS algorithm to be used as the nodes renumbering algorithm.     

一类特殊的分式规划问题的ε-近似算法

本文针对一类特殊的分式规划问题基于网格搜索提出了一个求其全局最优解的算法,且从理论上证明了算法的收敛性与计算复杂性,通过算例验证了算法的可行性与有效性.     

Analysis of Steiner subtrees of random trees for traceroute algorithms

We consider in this article the problem of discovering, via a traceroute algorithm, the topology of a network, whose graph is spanned by an infinite branching process. A subset of nodes is selected according to some criterion. As a measure of efficiency of the algorithm, the Steiner distance of the selected nodes, i.e. the size of the spanning subtree of these nodes, is investigated. For the selection of nodes, two criteria are considered: a node is randomly selected with a probability, which is either independent of the depth of the node (uniform model) or else in the depth biased model, is exponentially decaying with respect to its depth. The limiting behavior the size of the discovered subtree is investigated for both models. © 2009 Wiley Periodicals, Inc. Random Struct. Alg., 2009     

The distribution of points on the sphere and corresponding cubature formulae

In applications, for instance in optics and astrophysics, thereis a need for high-accuracy integration formulae for functionson the sphere. To construct better formulae than previouslyused, almost equidistantly spaced nodes on the sphere and weightsbelonging to these nodes are required. This problem is closelyrelated to an optimal dispersion problem on the sphere and tothe theories of spherical designs and multivariate Gauss quadratureformulae. We propose a two-stage algorithm to compute optimal point locationson the unit sphere and an appropriate algorithm to calculatethe corresponding weights of the cubature formulae. Points aswell as weights are computed to high accuracy. These algorithmscan be extended to other integration problems. Numerical examplesshow that the constructed formulae yield impressively smallintegration errors of up to 10^-12.     

求解通信网节点间全部路由的逻辑代数化算法

经典的D IJKSTRA和BELLM AN-F LOYD通信网络路由算法,只能根据特定网络参数得到最佳路由,却无法获得网络存在的全部可用路由,而通信网理论研究及网络管理等方面,往往需要获得节点之间的全部可用路由.研究出一种路由新算法,遵循逻辑代数运算规则、采用关联矩阵中行与行之间整合与删除方式计算,N个节点的网络只需N-1次整合及删除运算,就能得到源节点到任意节点两点之间全部路由结果.详细论证了算法的正确性与合理性,简介了算法的并行运算可行性及与经典路由算法的兼容性等问题.通过算例详细说明算法的计算过程,并验证其正确性.     

Structural balance in fully signed networks

Node attributes play an important role in shaping network structures, but are generally ignored in transformations of structural balance. A fully signed network consisting of signs of edges and nodes expresses both properties of relationship and node attributes. In this article, we generalize the definition of structural balance in fully signed networks. We transform the unbalanced fully signed network by not only changing signs of edges but also changing the signs of nodes. We propose a memetic algorithm to transform unbalanced networks at the lowest cost. Experiments show that our algorithm can solve this problem efficiently, and different node attribute assignments may lead to different optimized structures. © 2016 Wiley Periodicals, Inc. Complexity 21: 497–511, 2016     

Combining Swaps and Node Weights in an Adaptive Greedy Approach for the Maximum Clique Problem

In this work, the NP-hard maximum clique problem on graphs is considered. Starting from basic greedy heuristics, modifications and improvements are proposed and combined in a two-phase heuristic procedure. In the first phase an improved greedy procedure is applied starting from each node of the graph; on the basis of the results of this phase a reduced subset of nodes is selected and an adaptive greedy algorithm is repeatedly started to build cliques around such nodes. In each restart the selection of nodes is biased by the maximal clique generated in the previous execution. Computational results are reported on the DIMACS benchmarks suite. Remarkably, the two-phase procedure successfully solves the difficult Brockington-Culberson instances, and is generally competitive with state-of-the-art much more complex heuristics.