XL算法的冗余分析与改进

针对多变量二次方程组的求解问题,对XL算法的冗余性进行分析与改进.用XL算法扩展方程组存在冗余现象,采用该算法扩展由m个方程构成的n元二次方程组,所得到的新方程组中线性独立方程个数的上界为[mn(n+3 )-m( m-3)]/2.基于此,对XL算法进行改进.分析表明,改进后的XL算法能降低求解多变量二次方程组的计算复杂...     

基于分辨矩阵的快速完备约简算法

对分辨矩阵求核过程进行改进与扩展,给出了一种以属性频度作为启发式信息计算最小约简快速完备方法。与其它最小约简算法相比,该算法在很大程度上降低了算法的复杂度,提高了算法的效率。     

一种新的不一致决策表的属性约简算法

在基于正域的不一致决策表属性约简算法中,计算正域的算法效率是关键,直接影响到属性约简算法的时间复杂度。针对这一问题,新算法改进了区分矩阵的构造过程,提出了一种有效的在二进制区分矩阵上计算负域的方法,将约简的关键转换为对负域的计算,以属性频率为启发式信息指导属性约简过程。该算法也适用于一致决策表的属性约简。最后,通过实例证明了算法的有效性。     

基于启发式的粗糙集属性约简算法研究

对目前常见的粗糙集属性约简算法进行了研究和总结,在此基础上,针对差别矩阵以及启发式约简算法提出了改进算法,减少算法在计算时所需的时间和空间复杂度,求取最小约简。将改进后的约简算法系统地应用到学生考试成绩分析中,对得到的规则进行科学地评价,找出影响学生成绩的潜在因素,并提出学习建议。通过实际应用表明了改进算法的有效性和可行性。     

一种增量更新算法在数据挖掘中的应用

引入扩展差别矩阵和扩展决策矩阵，提出了新的属性约简算法和增量更新算法，即基于扩展差别矩阵的属性约简算法和基于扩展决策矩阵的增量式规则提取算法，讨论了规则的增量更新算法。由于使用了增量更新算法和并行处理技术，从而提高了数据挖掘的效率，降低了时间复杂度。通过实验说明此算法是有效和可行的。     

一种基于模糊理论和条件熵的属性近似约简的方法

给出了一种基于信息系统中连续型属性的模糊相似关系的定义以及相对应的关系矩阵,为了降低计算量对Warshall算法进行了改进。从信息论的角度提出了基于条件信息熵的属性新的近似相对约简集的概念和对应的约简算法,分析了算法的复杂度。实例和算法比较说明该算法是有效的。     

基于扩展的信息熵的决策表属性约简算法

从一种扩展的信息观的角度出发，讨论了Rough集理论的信息论观点。提出了一种基于扩展的信息熵的决策表核属性计算算法．并设计了以属性重要性为启发信息的自下而上的决策表属性约简算法EIEAAR。同时针对不一致表，将属性对不相客对象的包含值作为第二标准选择属性以加快约简速度。EIEAAR算法能处理一致和不一致决策表，并将核属性计算和非核属性约简统一起来。最后，对算法进行复杂度分析并用实例验证算法的有效性。实验表明该算法能有效得到决策表的最小约简。     

改进的布尔冲突矩阵的高效属性约简算法

近年来,诸多学者喜欢用差别矩阵的方法来设计属性约简的算法,但由于计算差别矩阵不仅费时且还浪费空间,导致这些属性约简算法都不够理想。为了降低属性约简算法的复杂度,在布尔冲突矩阵的基础上,定义了一个启发函数,该函数能求出决策表中条件属性导致的冲突个数,同时给出了计算该启发函数的快速算法。然后用该启发函数设计了一个有效的基于改进的布尔冲突矩阵的不完备决策表的高效属性约简算法,该算法能够有效降低时间复杂度。最后实验结果说明了新算法的有效性。     

基于粗糙集和信息增益的属性约简改进方法

针对属性过多对于有效的数据挖掘很不利以及约简中差别矩阵的产生会占用较大存储空间的问题,提出了一种基于粗糙集和信息增益的属性约简改进算法.该算法首先采用信息增益技术对决策表属性进行相关分析,删除部分冗余属性,减小属性约简的复杂度,然后直接从决策表中提取出分明函数,求出属性约简.由于避免了分明矩阵的生成,因此该算法不仅节约了时间和空间,而且提高了效率.     

一种改进的属性约简算法

粗糙集理论是一种有效的信息处理工具,属性约简是粗糙集理论研究的一个核心内容。为了能够较为有效地获得不相容决策表较优的属性约简,在对文献[7]中属性约简算法分析的基础上,根据不相容决策表约简不改变决策表正域的原则,仅考虑相对差异比较表中与正域相关的实例对,同时结合属性重要性作为特征选取的启发式信息,提出了一种改进的启发式属性约简算法。该算法在不增加算法时间复杂度的前提下能够处理不相容决策表。最后,通过实例完整演示了该方法,表明该算法是有效的。     

Asymptotic Forms and Algebraic Differential Equations

We analyse the complexity of a simple algorithm for computing asymptotic solutions of algebraic differential equations. This analysis is based on a computation of the number of possible asymptotic monomials of a certain order, and on the study of the growth of this number as the order of the equation grows.     

Toric ideals and graph theory to analyze Hopf bifurcations in mass action systems

A family of polynomial differential systems describing the behavior of a chemical reaction network with generalized mass action kinetics is investigated. The coefficients and monomials are given by graphs. The aim of this investigation is to clarify the algebraic-discrete aspects of a Hopf bifurcation in these special differential equations. We apply concepts from toric geometry and convex geometry. As usual in stoichiometric network analysis we consider the solution set as a convex polyhedral cone and we intersect it with the deformed toric variety of the monomials. Using Gröbner bases the polynomial entries of the Jacobian are expressed in different coordinate systems. Then the Hurwitz criterion is applied in order to determine parameter regions where a Hopf bifurcation occurs. Examples from chemistry illustrate the theoretical results.     

Analysis of nonlinear electrical circuits using bernstein polynomials

In electrical circuit analysis, it is often necessary to find the set of all direct current (d.c.) operating points (either voltages or currents) of nonlinear circuits. In general, these nonlinear equations are often represented as polynomial systems. In this paper, we address the problem of finding the solutions of nonlinear electrical circuits, which are modeled as systems of n polynomial equations contained in an n-dimensional box. Branch and Bound algorithms based on interval methods can give guaranteed enclosures for the solution. However, because of repeated evaluations of the function values, these methods tend to become slower. Branch and Bound algorithm based on Bernstein coefficients can be used to solve the systems of polynomial equations. This avoids the repeated evaluation of function values, but maintains more or less the same number of iterations as that of interval branch and bound methods. We propose an algorithm for obtaining the solution of polynomial systems, which includes a pruning step using Bernstein Krawczyk operator and a Bernstein Coefficient Contraction algorithm to obtain Bernstein coefficients of the new domain. We solved three circuit analysis problems using our proposed algorithm. We compared the performance of our proposed algorithm with INTLAB based solver and found that our proposed algorithm is more efficient and fast.     

Solving systems of polynomial equations

Geometric and solid modelling deal with the representation and manipulation of physical objects. Currently most geometric objects are formulated in terms of polynomial equations, thereby reducing many application problems to manipulating polynomial systems. Solving systems of polynomial equations is a fundamental problem in these geometric computations. The author presents an algorithm for solving polynomial equations. The combination of multipolynomial resultants and matrix computations underlies this efficient, robust and accurate algorithm     

一种引入动量项的变步长LMS算法的研究

该文针对SVSLMS算法步长函数在误差e（n）接近零处不具有缓慢变化的缺点和MLMS算法由于采用固定步长使得在稳态阶段权值更新到期望值速度过慢的不足进行了讨论。通过更新SVSLMS算法步长函数和在权值调整式中增加动量项，该文提出了一种改进算法—SVS-MLMS算法。该算法具有步长函数在误差e（n）接近零处能够缓慢变化的优点，使得在白适应稳态阶段的步长稳定在最优值，进而使权值收敛到最佳。仿真结果证明该算法在学习曲线收敛速度加快和稳态误差减小方面取得了较好的效果。该文还讨论了算法中三个参数a，b，r的取值对算法收敛性能的影响，确定了它们的最优值。     

Elimination of Constraint Violation and Accuracy Aspects in Numerical Simulation of Multibody Systems

Multibody systems are often modeled as constrained systems, and theconstraint equations are involved in the dynamics formulations. To makethe arising governing equations more tractable, the constraint equationsare differentiated with respect to time, and this results in unstablenumerical solutions which may violate the lower-order constraintequations. In this paper we develop a methodology for numerically exactelimination of the constraint violations, based on appropriatecorrections of the state variables (after each integration step) withoutany modification in the motion equations. While the elimination ofviolation of position constraints may require few iterations, theviolation of velocity constraints is removed in one step. The totalenergy of the system is sometimes treated as another measure of theintegration process inaccuracy. An improved scheme for one-stepelimination of the energy constraint violation is proposed as well. Theconclusion of this paper is, however, that the energy conservation is ofminor importance as concerns the improvement of accuracy of numericalsimulations. Some test calculations are reported.     

改进变步长算法在实时飞行仿真中的应用

飞行模拟机是民航训练飞行员的重要装备,飞行仿真系统是飞行模拟机的重要系统之一.飞行仿真要建立飞机的全量运动方程,利用数值算法解算运动方程达到仿真飞机飞行状况的目的.采用四元数法表示的飞机欧拉方程能够克服普通欧拉方程奇异性,但用定步长方法解算会产生较大累积误差,所以必须采用变步长方法.实时飞行仿真要求较高的实时性与逼真度,通过仿真试验分析,确定了采用一种改进变步长2阶Runge-Kutta法,该方法具有迭代次数少,解算精度高,实时性强的优点.利用该改进变步长算法,编写了实时飞行系统仿真软件,软件中使用相应算法解决了变步长算法选择步长与系统迭代定时时间不匹配的矛盾,实现了精确的实时仿真.     

A combined method for enclosing all solutions of nonlinear systems of polynomial equations

We consider the problem of finding interval enclosures of all zeros of a nonlinear system of polynomial equations. We present a method which combines the method of Gröbner bases (used as a preprocessing step), some techniques from interval analysis, and a special version of the algorithm of E. Hansen for solving nonlinear equations in one variable. The latter is applied to a triangular form of the system of equations, which is generated by the preprocessing step. Our method is able to check if the given system has a finite number of zeros and to compute verfied enclosures for all these zeros. Several test results demonstrate that our method is much faster than the application of Hansen’s multidimensional algorithm (or similar methods) to the original nonlinear systems of polynomial equations.     

Automatic time stepping algorithms for implicit numerical simulations of non-linear dynamics

When an implicit integration scheme is used, variable step strategies are especially well suited to deal with problems characterized by high non-linearities. Constant step size strategies generally lead to divergence or extremely costly computations. An automatic time stepping algorithm is proposed that is based on estimators of the integration error of the differential dynamic balance equations. Additionally, the proposed algorithm automatically takes decisions regarding the necessity of updating the tangent matrix or stopping the iterations, further reducing the computational cost. As an illustration of the capabilities of this algorithm, several numerical simulations of both academic and industrial problems are presented.     

Improved D‐Type Anticipatory Iterative Learning Control for a Class of Inhomogeneous Heat Equations

This paper aims at providing a practical iterative learning control (ILC) scheme for a wide class of heat transfer systems in the sense that it avoids high‐gain learning of ILC, thus a potential non‐monotonic convergence issue, and the risk of violating the hardware limitation of input profile in implementation. Meanwhile, the ILC scheme guarantees the identical initial condition of heat process. As a result, the output tracking precision may be improved while not reducing the anticipatory step size as in 1 . All the benefits of the proposed ILC scheme are achieved by applying a heuristic selection algorithm for the anticipatory step size and rectifying the output reference simultaneously.