用神经网络计算矩阵特征值与特征向量

该文研究用神经网格求解一般实对称矩阵的全部特征向量的问题。详细讨论了网络的平均态度合的结构并建立了平衡态集合的构造定理。通过求解简单的一维微分方程求出了网络的解析表达式。这一表达式是由对称矩阵的特征值与特征向量表达的、因而非常清晰利用解的解析表达式分析了网络的解的全局渐近行为。提出了用一些单位向量作为网络初始值计算对称矩阵的全部特征值与特征向量的具体算法。     

基于结式法计算目标的空间方位

根据图像信息确定立体目标的空间方位是计算机视觉中的一个基本问题。利用图像亮度的二维矩将该问题可以化为七个六变元的非线性多项式方程组。此文提出利用结式法求解该方程组的闭形式解。该方法一次可以消去多个变元,克服了传统方法中逐个消去变元的弊端,提高了算法的效率。除此之外,我们的方法是确定的构造性算法,并且发挥了结式理论在符号消元方面的优势。因而,该方法高效地解决了目标空间定位中的相关计算。     

粒度计算方法

粒度计算是一种用来处理不完全、不可靠、不精确、不一致和不确定知识的工具,它象一把大伞,覆盖了所有有关粒度的理论、方法论、技术和工具的研究,已成为人工智能研究领域的重要热点。本文从人类智能特点出发,分析了粒度的特征,提出了商空间理论的粒度计算模型。介绍了粒度计算的主要方法,并对这些方法进行了比较。     

三对角矩阵的行列式的并行计算方法

文章针对三对角矩阵,利用矩阵的Schur余子式求矩阵行列式的方法,提出了一种并行求解三对角矩阵及其逆的行列式的算法,应用该算法可以得到较好的加速度。     

可分辨矩阵及其求核方法

为解决因决策表中存在不相容性导致的求核错误问题,提出一种将不相容决策表转化为相容决策表的定义形式。根据该定义创建可分辨矩阵,并给出求核方法,同时证明该方法获得的核与正区域的核是一致的。设计求核算法,该算法既适用于相容决策表,也适用于不相容的决策表。实例表明该算法是有效的。     

网络系统可靠度的连接矩阵逻辑扩展算法

针对网络性能优化技术,着重研究无线网络传输可靠性问题,为有效提高3-状态无圈有向设备网络系统二终端可靠度仿真算法效率;采用网络的连接矩阵表示形式,在定义了连接矩阵列变换后,依据连接矩阵逻辑扩展技术对连接矩阵实施连续的代数变换,得到了求3-状态设备网络二终端可靠度的一个有效快速算法。仿真示例表明,使网络系统可靠度符号表达式中项数大幅度减少,算法效率显著提高。由于算法使用了网络系统的代数化表示方法,结合了消除冗余项存储及简化技术,算法具有节约存储空间、执行效率高特点。对复杂网络系统可靠度评估具有重要参考价值。     

Computing the Matrix Mittag-Leffler Function with Applications to Fractional Calculus

The computation of the Mittag-Leffler (ML) function with matrix arguments, and some applications in fractional calculus, are discussed. In general the evaluation of a scalar function in matrix arguments may require the computation of derivatives of possible high order depending on the matrix spectrum. Regarding the ML function, the numerical computation of its derivatives of arbitrary order is a completely unexplored topic; in this paper we address this issue and three different methods are tailored and investigated. The methods are combined together with an original derivatives balancing technique in order to devise an algorithm capable of providing high accuracy. The conditioning of the evaluation of matrix ML functions is also studied. The numerical experiments presented in the paper show that the proposed algorithm provides high accuracy, very often close to the machine precision.     

一个基于差别矩阵的快速求核算法

给出简化差别矩阵和相应核的定义,并证明该核与差别矩阵的核是等价的。在此基础上设计了一个新的求核算法,使得新算法的时间复杂度和空间复杂度分别被降为max｛O(CU/C2),O(CU)｝和max｛O(U),O(CU/C2)｝。     

一种加权计算基础矩阵的高精度算法

分析了图像匹配点对基础矩阵的不同影响,引入具有明显几何意义的匹配点到对极线的距离作为匹配点的加权因子,将匹配点集合看作随机变量并将加权因子作为匹配点的概率分布。在此基础上对原始图像数据进行归一化处理,利用8点算法得到基础矩阵。大量的试验结果表明,该方法明显降低了计算余差,提高了基础矩阵的计算精度。     

Ordered Line Integral Methods for Computing the Quasi-Potential

The quasi-potential is a key function in the Large Deviation Theory. It characterizes the difficulty of the escape from the neighborhood of an attractor of a stochastic non-gradient dynamical system due to the influence of small white noise. It also gives an estimate of the invariant probability distribution in the neighborhood of the attractor up to the exponential order. We present a new family of methods for computing the quasi-potential on a regular mesh named the ordered line integral methods (OLIMs). In comparison with the first proposed quasi-potential finder based on the ordered upwind method (OUM) (Cameron in Phys D Nonlinear Phenom 241:1532–1550, 2012), the new methods are 1.5–4 times faster, can produce error two to three orders of magnitude smaller, and may exhibit faster convergence. Similar to the OUM, OLIMs employ the dynamical programming principle. Contrary to it, they (1) have an optimized strategy for the use of computationally expensive triangle updates leading to a notable speed-up, and (2) directly solve local minimization problems using quadrature rules instead of solving the corresponding Hamilton–Jacobi-type equation by the first order finite difference upwind scheme. The OLIM with the right-hand quadrature rule is equivalent to OUM. The use of higher order quadrature rules in local minimization problems dramatically boosts up the accuracy of OLIMs. We offer a detailed discussion on the origin of numerical errors in OLIMs and propose rules-of-thumb for the choice of the important parameter, the update factor, in the OUM and OLIMs. Our results are supported by extensive numerical tests on two challenging 2D examples.     

文化计算方法与应用综述

文化计算是把计算及相关技术应用到文化领域,探索其中的发展规律、揭示其中的内在联系或对其进行可视分析与展示.因此,文化计算对于文化的本质挖掘和传承发扬都具有重大意义.论文对文化计算做了简单概述.首先,从文化基因的内涵解析入手,以文化组学为理论,对文化计算的演化脉络和其发展历程进行总结;介绍了一些有相似思想的文章进行文化计算理论的延展,并对文化计算的方法进行比较.其后重点阐述了文化计算的研究内容,包括作为信息基本模式的文化基因、核心研究对象文化量化以及可视分析的大数据应用方法,分析各研究内容是如何对文化进行量化计算、科学分析的.最后应用案例介绍了文化计算的应用,并对文化计算进行了总结与展望.     

非线性二次矩阵方程的多分裂法

本文针对系数矩阵为方阵的非线性二次矩阵方程AX2+BX+C=0,结合多分裂法及牛顿法,给出了二次矩阵方程的两种迭代算法。同时,运用积分中值定理,对所得算法的收敛性进行了分析,得到相应算法的收敛性定理。最后,通过数值示例,对文中论述进行了强有力的验证。     

基于LogP简化模型的矩阵求逆并行算法研究

LogP is becoming a practical parallel computation model that meets the demanding of parallel computers and parallel algorithms. So it is important to re-design parallel algorithms on the LogP model. This paper studies the parallel algorithm of computing converse matrix on the simplified LogP model, and gets the simulating results.     

Computing the Maximum Degree of Minors in Matrix Pencils via Combinatorial Relaxation

This paper presents a new algorithm for computing the maximum degree δk (A) of a minor of order k in a matrix pencil A(s) . The problem is of practical significance in the field of numerical analysis and systems control. The algorithm adopts a general framework of ``combinatorial relaxation'' due to Murota. It first solves the weighted bipartite matching problem to obtain an estimate $\hat{\delta}_k(A)$ on δk (A) , and then checks if the estimate is correct, exploiting the optimal dual solution. In case of incorrectness, it modifies the matrix pencil A(s) to improve the estimate $\hat{\delta}_k(A)$ without changing δk(A) . The present algorithm performs this matrix modification by an equivalence transformation with constant matrices, whereas the previous one uses biproper rational function matrices. Thus the present approach saves memory space and reduces the running time bound by a factor of rank A.     

Numerical Inversion Methods for Computing Approximate p-Values

The paper considers the problem of computing p-values of non-standard distributions for which the characteristic function is available in closed form. When the characteristic function is a multivalued complex function, the standard numerical inversion method needs to be used with care as the integrand may become discontinous due to branch cuts. An alternative inversion method based on the Gaver-Wynn-Rho algorithm is shown to be a general and effective solution to the discontinuity problem as it works with real-valued functions. The method is illustrated with two well-known time series tests with non-standard distributions. JEL classification: C40; C12 An erratum to this article can be found at     

志愿计算模型形式化方法

旨在从形式化抽象的角度来认识移动计算的本质特点.分析了志愿计算平台的特征,提出并分析了志愿计算中的3种角色以及志愿计算中资源和构件的概念,介绍了一种关于志愿计算的形式化模型和方法.对系统中的基本元素和交互关系进行了形式化的描述,并通过集合理论和操作规约,又以志愿计算平台XtremWeb为例,描述了构件化的志愿计算形式模型和方法,为系统地研究志愿计算形式化理论打下了基础.     

一个基于修正的二进制差别矩阵的快速求核方法

本文研究了二进制差别矩阵中核属性的性质,指出并证明了二进制差别矩阵求核的理论依据,在此基础上给出了一种二进制差别矩阵的修正方法及求核方法。该方法不仅适用于任何决策表信息系统（相容决策表和不相容决策表）,而且有效地降低了计算代价。