关键词： LINEAR PROGRAMMING   POLYNOMIAL-TIME ALGORITHMS   STRONGLY POLYNOMIAL-TIME ALGORITHMS   CIRCULANT MATRICES   ALGEBRAIC NUMBERS  

摘要： We show that a modified variant of the interior point method can solve linear programs (LPs) whose coefficients are real numbers from a subring of the algebraic integers. By defining the encoding size of such numbers to be the bit size of the integers that represent them in the subring, we prove the modified algorithm runs in time polynomial in the encoding size of the input coefficients, the dimension of the problem, and the order of the subring. We then extend the Tardos scheme to our case, obtaining a running time which is independent of the objective and right-hand side data. As a consequence of these results, we are able to show that LPs with real circulant coefficient matrices can be solved in strongly polynomial time. Finally, we show how the algorithm can be applied to LPs whose coefficients belong to the extension of the integers by a fixed set of square roots.

关键词： MATRIX ALGEBRA   ALGORITHMS  

摘要： The letter presents a new recursive algorithm for solving linear algebraic equations Ax = b. With this algorithm, the ith step recursion can find one solution of the first i equations;the unique solution of the total n equations could be found after the nth step recursion. Because of this recursive property, the algorithm can be used not only in solving ill-conditioned equations but also in recursive identification, signal processing and many other areas.

关键词： 辨识   评价函数   矩阵方程   连续系统  

摘要： 本文将给出近似计算连续系统传递函数系数的方法,而且只要原系统是稳定的,则可以保证用这种方法得到的近似模型也是稳定的。

摘要： The paper elucidates the internal properties of some iterative linear algebra algorithms through transformation of their lattice graphs.

摘要： An explicit parametrization algorithm is reported for the simplest class of triply periodic minimal surfaces (the 'regular' class) for which the Weierstrass function specifying the complex plane representation has a simple product form. As the Gauss map links triply periodic minimal surfaces with spherical tessellations, the set of Schwarz triangular tilings of the sphere is used as the basis of an exhaustive listing of all such possible branch-point distributions, and hence surfaces, in this class. The symmetry and geometry of the resulting surfaces are determined by the locations and orders of these branch points.

关键词： 巨型机   数学库   逻辑   并行算法  

摘要： 本文介绍了巨型机通用数学库软件的概念和意义,指出了巨型机数学软件开发的技术途径与发展趋势,讨论了并行算法在其中的关键性作用,结合实例分析了巨型机通用数学库软件研制中的并行算法设计与实现。

关键词： 排队网络系统   数学规划   算法  

摘要： 一、问题的提出 复杂随机服务系统的优化或规划设计问题,因系统和运行环境的复杂性及随机性,一般都采用计算机模拟技术。如果把N个随机服务系统组成一个复杂的排队网络系统,用计算机模拟也能得到比较好的解决。可是,当每个子系统的状态都比较多(设i子系统的状态数为S_i),因为模拟技术不能直接求最优解这一固有缺陷,要确定系统的最优运行状态就必须把所有各子系统不同状态之间的匹配情况都进行模拟(这便需要对整个系统模拟S_1 S_2…S_N次),然后再比较各次模拟结果,从中选出最优解。如果系统的状态数较大或一次模拟花费的机时较长,则S_1 S_2…

关键词： 配电系统   可靠性   数学模型   算法  

摘要： 本文提出了一种10kV 配电系统可靠性数学模型,模型中考虑了切换操作、母线故障、T 接的影响、计划检修等因素。在此基础上,应用增流减流交叉网流法,发展了一种大型10kV 配电系统可靠性评估的快速算法,形成了相应的实用软件,并开始在国内实现了10kV 配电系统可靠性的工程应用,展现了这一技术的发展前景。

关键词： 凸轮   函数方程   CAD   算法  

摘要： 本文建立了凸轮廓线的数学模型.利用一个活动坐标系可以很方便地建立凸轮各段运动轨迹的连接方程,并可对尖点进行修改.文中详述了上述数学处理方法及算法.