New doubling algorithm for the discrete periodic Riccati Equation

The periodic Riccati equation that results from periodic state space models plays an important role in many fields of mathematics, science, and engineering. In most applications, it is essential that the solution to the Riccati equation be obtained in the shortest possible time. Such a computationally effective doubling algorithm that solves the discrete periodic Riccati equation is proposed in this paper. Moreover, the memory requirements and the calculation burden needed for the sequential implementation of the proposed algorithm are established, and compared to the memory requirements and the calculation burden needed for the sequential implementation of classical algorithms. The basic conclusion of the above comparison is that the calculation time required to solve the periodic Riccati equation using the classical algorithms is in general much greater than the calculation time required to solve the periodic Riccati equation by using the proposed algorithm. Finally, the numerical behavior of the proposed algorithm is tested through simulation examples. It is established that the proposed algorithm is fast, computationally efficient, and numerically stable, and possesses very good parallelism efficiency.     

一种求解救灾物资运输问题的改进解法

本文通过对B运输问题建立数学模型,提出了一种求解B运输问题的改进解法。改进解法首先通过最小元素法求出初始解,然后进行变量闭回路法调整,直到求出最优解,并给出了一个计算实例证明了解法的有效性。文章还对改进解法和另外两种现有的算法进行了综合的分析,由于改进解法计算过程中采用的变量闭回路法省略了求检验数的环节,使得新算法比两种现有的算法更简便。     

基于部分基变量的LP问题矩阵算法

基于部分基变量提出了LP问题的矩阵算法. 该算法以最优基矩阵的一个充分必要条件为基础,首先将一个初始矩阵转化为右端项和检验数均满足要求的矩阵,再转为检验数满足要求的基矩阵,最后转化为最优基矩阵.该算法具有使用范围广、计算规模小、计算过程简化、计算机易于实现的优势.矩阵算法的核心运算是求逆矩阵的运算,提出了矩阵算法的求逆问题,讨论并给出了求逆快速算法,该算法充分利用了矩阵算法迭代过程中提供的原来的逆矩阵的信息经过简单的变换得到新的逆矩阵,该算法比直接求逆法计算效率更高.     

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.     

周期三对角矩阵逆的一种新算法

给出了一类周期三对角矩阵逆的新的递归算法.新方法充分利用周期三对角矩阵的结构特点,采用递归方法将高阶周期三对角矩阵求逆转化为低阶周期三对角矩阵的求逆.并同时得到简化的计算方法,方法可以有效地减少运算量和存储量,计算精度也有明显的优势.数值实验表明此算法是有效的.     

Calculation of Posterior Bounds Given Convex Sets of Prior Probability Measures and Likelihood Functions

Abstract

This article presents alternatives and improvements to Lavine's algorithm, currently the most popular method for calculation of posterior expectation bounds induced by sets of probability measures. First, methods from probabilistic logic and Walley's and White-Snow's algorithms are reviewed and compared to Lavine's algorithm. Second, the calculation of posterior bounds is reduced to a fractional programming problem. From the unifying perspective of fractional programming, Lavine's algorithm is derived from Dinkelbach's algorithm, and the White-Snow algorithm is shown to be similar to the Charnes-Cooper transformation. From this analysis, a novel algorithm for expectation bounds is derived. This algorithm provides a complete solution for the calculation of expectation bounds from priors and likelihood functions specified as convex sets of measures. This novel algorithm is then extended to handle the situation where several independent identically distributed measurements are available. Examples are analyzed through a software package that performs robust inferences and that is publicly available.     

深入研究模糊逻辑的必要性与紧迫性

因为"取大取小"不是数学计算,所以基于"取大取小"的模糊逻辑不能为数值转换提供算法支撑,使得模糊理论面临无合适模型可用的被动境地.指出,模糊逻辑是逻辑的一个新的近似推理研究方向,它的量化方法是数值计算;目的是支撑隶属度转换,使得由指标隶属度确定的目标隶属度是"真值"在当前条件下的最优近似.模糊逻辑是在隶属度转换条件下对人类近似推理本领规范的一种方法.而进行规范的依据是区分权滤波的冗余理论,实质性计算是由冗余理论导出的、实现隶属度转换的非线性去冗算法;相应的隶属度转换模型是非线性数学模型.     

一种基于可拓学的电子商务内容推荐算法研究

为研究电子商务内容推荐算法,论文从电子商务推荐系统中的瓶颈问题——相似度计算出发,借助可拓学的方法进行分析。论文将可拓学中基元的表示方法引入推荐算法中,并采用关联函数和可拓距的思想,实现了产品的表示和相似度计算,进而得到了一种新的内容推荐算法。然后通过实例分析对算法进行验证,确认了方法的可靠性和有效性。论文的研究将可拓学思想引入到推荐算法中,这对可拓思想的应用以及推荐算法的实现都起到了有益的作用。     

Leave-two-out stability of ontology learning algorithm

Ontology is a semantic analysis and calculation model, which has been applied to many subjects. Ontology similarity calculation and ontology mapping are employed as machine learning approaches. The purpose of this paper is to study the leave-two-out stability of ontology learning algorithm. Several leave-two-out stabilities are defined in ontology learning setting and the relationship among these stabilities are presented. Furthermore, the results manifested reveal that leave-two-out stability is a sufficient and necessary condition for ontology learning algorithm.     

Simple signature based iterative algorithm for calculation of Gröbner bases

The paper presents an algorithm for calculation of Gröbner bases with the use of labeled polynomials from the F5 algorithm. The distinct feature of this algorithm is the simplicity both of the algorithm and the proof of its correctness achieved without loss of efficiency. This leads to a simple implementation whose performance is in par with more complex analogues.     

一个求大规模非负不可约稀疏矩阵的谱半径及特征向量的新算法

本文设计了一个计算非负不可约矩阵的谱半径及其特征向量的新算法,并证明了其收敛性.该算法计算晕不大,占用内存少,有相同的0元模式,从而在大规模稀疏矩阵的计算中优势明显.最后用实例验证了此算法的可行性.     

High Radix BKM Algorithm

In this paper, a high radix implementation of the BKM algorithm is introduced. The BKM algorithm is a shift-and-add CORDIC-like algorithm that performs fast computation of complex exponential and logarithm without any scalling factor. The proposed implementation reduces the number of iterations needed for the calculation. Compared to previous implementations of high radix BKM algorithm, it needs smaller lookup tables.     

Fractal analysis of time series in oil and gas production

The peculiarities of fractal characteristics’ calculations for time series are described in this article. An algorithm for calculation of fractal dimension is suggested. It has been proved that the suggested method possesses high accuracy and the rapidity of convergence on the limited number of measurements compared to the methods of covering.The criteria of early diagnosis for changes in the condition of hydrodynamic processes, which do not vary by fractal dimension, have been recommended.The presented method is applicable for practical engineering calculations with self-affine, chaotic data, usually with relatively limited number of measurements. It is quite a simple method for calculation of fractal dimension, algorithm can be easily realized and it should be useful for engineers.The applicability of the proposed algorithm for fractal dimension calculation and early diagnosis criteria of qualitative changes in the behaviour of various dynamic systems has been tested both on simulated as well as practical examples of oil and gas production.     

资源公平分配的一种贪婪算法

对资源公平分配模型提出了一种简单的贪婪算法，在一定条件下可得到全局最优解且在相当多的情况下所得解都为最优解。该方法效率极高，编程简单，计算量很小，从大量模拟情况来看相当有效。     

遗传算法的一种改进进化策略

在现有文献研究的基础上,对传统遗传算法的进化策略又作了进一步研究,提出了一种改进的进化策略.进化策略克服了传统遗传算法中交又得到的优秀个体有可能在变异过程中遭到破坏而不能生存的不足.另外取消了遗传算法中难以确定的交叉、变异概率,使交叉产生的新个体数增多,这样可增大产生更优秀个体的可能性,因而可使遗传算法的性能得到更好的改善.通过4个测试函数的测试计算,结果表明,给出的改进进化策略比传统遗传算法进化策略的运算速度明显提高,迭代次数明显减少,从而验证了提出的改进进化策略的有效性.     

Method of controlled models in the problem of reconstructing a boundary input

The problem of dynamic reconstruction of boundary controls in a nonlinear parabolic equation is considered. In the case of a control concentrated in the Neumann boundary conditions, a solution algorithm is described, which is stable with respect to the information noise and calculation errors. The algorithm is based on the construction of feedback-controlled auxiliary models.     

A two-step algorithm of smooth spline generation on Riemannian manifolds

This paper presents a simple geometric algorithm to generate splines of arbitrary degree of smoothness in Euclidean spaces. Unlike other existing methods, this simple geometric algorithm does not require a recursive procedure and, consequently, introduces a significant reduction in calculation time. The algorithm is then extended to other complete Riemannian manifolds, namely to matrix Lie groups and spheres.     

Face recognition based on a matching algorithm with recursive calculation of oriented gradient histograms

A face recognition method based on a matching algorithm with recursive calculation of oriented gradient histograms for several circular sliding windows and a pyramidal image decomposition is proposed. The algorithm produces good results for geometrically distorted and scaled images.     

考虑传输容量的通信网端到端可靠性指标算法

归一化传输容量加权通信网端到端可靠性指标,非常适合评价现代高速宽带通信网络.然而计算全过程易于在计算机上编程实现的算法尚未见到.研究出一整套可靠性指标的计算方法.由于,从路由计算、不交化网络状态集及其对应容量的求取,到最后获得可靠性指标结果等各个环节,均实现了代数化或逻辑代数化运算,因此,整套算法易于编写计算机程序.详细介绍了算法各环节的计算规则与步骤,并对正确性与合理性进行了论证.通过举例详细说明算法的计算过程,并检验算法的正确性.     

The Hurwitz determinants and the signatures of irreducible representations of simple real Lie algebras

The paper deals with the real classical Lie algebras and their finite dimensional irreducible representations. Signature formulae for Hermitian forms invariant relative to these representations are considered. It is possible to associate with the irreducible representation a Hurwitz matrix of special kind. So the calculation of the signatures is reduced to the calculation of Hurwitz determinants. Hence it is possible to use the Routh algorithm for the calculation.