最佳逼近圆周的正多边形算法

本文定义了圆周的最佳逼近正n边形，在上述意义下，解决了圆周的最佳逼近正n边形半径的计算问题。     

最佳逼近圆周的正多边形算法(Ⅲ)

利用渐近平均距离定义了圆周的最佳逼近正多边形 ,在上述意义下 ,解决了圆周的最佳逼近正多边形半径R的计算问题     

最佳逼近圆周的正多边形算法(Ⅲ)

利用渐近平均距离定义了圆周的最佳逼近正多边形,在上述意义下,解决了圆周的最佳逼近正多边形半径R的计算问题.     

Said-Bézier曲线的等距曲线的有理逼近

等距曲线逼近的关键在于对其参数速度的逼近,给出了Said-Bezier曲线参数速度的Tchebyshev逼近和Tchebyshev-Pade逼近,在此基础上得到了Said-Bezier曲线的等距曲线的2种有理逼近函数.因为n次Said-Bezier曲线在参数K=[n/2]时,即为,1次Bezier曲线,所以文中方法同样适用于Bezier曲线的等距曲线逼近.最后通过2个实例验证了这2种逼近方法,并与Legendre逼近方法进行了比较.     

自适应最佳多项式逼近的Remes算法

在函数数值逼近中,常以代数多项式作为逼近工具,而在各种多项式逼近的方法中,尤以最佳多项式逼近倍受重视。在计算机被广泛使用以前,人们多只能用Tayl?r展开、Chebyshev展开等方法。最佳逼近算法对于手工计算而言,巨大的运算量令人望而却步。即使在计算机高度发展的今天,如果算法的实现不甚考究,所耗费机时仍嫌过多。本文的     

线性流形上一类矩阵方程的最佳逼近问题

本文研究矩阵方程AXB=C在线性流形Γ={X∈SR~(n×n)|||TX-Y||=min}上的最佳逼近问题,得到了问题解的表达式．此外,还给出了求解该问题的数值算法和算例．     

埃尔米特自反矩阵的广义逆特征值问题与最佳逼近问题

在振动控制中,通常用矩阵的逼近问题来校正刚度矩阵和质量矩阵,使得它们具有给定的谱约束条件.本文基于埃尔米特自反矩阵的表示定理,利用矩阵的拉直和Kronecker积,得到了埃尔米特自反矩阵广义逆特征值问题解的一般表达式.进一步,对任意给定的n阶复矩阵对,利用Moor-Penrose广义逆和逼近理论,得到了其相关最佳逼近问题解的表达式.     

一种分数阶微积分算子的有理函数逼近方法

基于有理函数逼近理论, 提出了一种分数阶微积分算子s域最佳有理逼近函数的构造方法. 详细讨论了构造最佳有理逼近函数的思路、方法及具体算法. 运用最佳有理逼近定义及特征定理, 对所构造的分数阶积分算子最佳有理逼近函数进行了验证. 其结果表明:该分数阶微积分算子最佳有理逼近函数构造方法是有效的, 且对确定的逼近误差及逼近频带, 所构造的最佳有理逼近函数能够以最低阶次取得最佳逼近特性.     

构造前向神经网络逼近多项式函数

首先用构造性的方法证明:对于任意的n阶多元多项式函数,可以构造一个三层前向神经网络以任意精度逼近该多项式,所构造网络的隐层节点个数仅与多项式的维数d和阶数n有关.然后,我们给出实现这一逼近的具体算法.最后,给出两个算例进一步验证所得的理论结果.本文结果对神经网络逼近多元多项式函数的具体网络构造以及实现这一逼近的方法等问题具有指导意义.     

对DES线性攻击的改进算法

给出了DES的两个较大的14轮线性逼近,它们的相关系数分别为最佳线性逼近相关系数的0.8倍和0.6倍,且涉及到完全相同的密钥和不同的明密文。结合这两个较好的线性逼近,提出了攻击DES的改进算法,利用改进后的算法可以在等量明密文对的情况下多得到9比特密钥值。     

圆的等面积逼近和生成

本文描述用多边形等面积逼近和生成圆的算法，此算法是用一个与圆相交的多边形（而不是通常用的内接多边形）逼近一个圆，这个多边形的面积精确地等于圆的面积。因此，可以认为这种算法产生的多边形是对圆的一种等面积最佳逼近。     

Ring-coupled unicycles: Boundedness, convergence, and control

In cyclic pursuit a platoon of vehicles are coupled in a unidirectional ring at the interaction level according to some control scheme. In the paper, a new cyclic pursuit control law is proposed, where each vehicle’s linear speed and angular speed are proportional to the projection of its prey’s position on its forward direction and lateral direction respectively. Through these interactions a cooperative behavior emerges and vehicles in the platoon eventually move at a constant speed on a circle with constant inter-vehicle spacings. The control scheme ensures ultimate boundedness and leads to only two stable equilibrium polygons. This contrasts with other cyclic pursuit control schemes, where vehicles may diverge to infinity and there are more stable equilibrium polygons as the total number of vehicles increases. For this control scheme, ultimate boundedness is proved using the pseudo-linearization technique. Possible equilibrium polygons are analyzed and stability and convergence properties are established through root locus analysis of a complex characteristic polynomial. Design rules are discussed, showing how the radius of the circle they converge to is controlled by an appropriate choice of control parameters.     

Fast Algorithms for Computing the Smallest k-Enclosing Circle

For a set $P$ of $n$ points in the plane and an integer $k \leq n$, consider the problem of finding the smallest circle enclosing at least $k$ points of $P$. We present a randomized algorithm that computes in $O( n k )$ expected time such a circle, improving over previously known algorithms. Further, we present a linear time $\delta$-approximation algorithm that outputs a circle that contains at least $k$ points of $P$ and has radius less than $(1+\delta)r_{opt}(P,k)$, where $r_{opt}(P,k)$ is the radius of the minimum circle containing at least $k$ points of $P$. The expected running time of this approximation algorithm is $O(n + n \cdot\min((1/k\delta^3) \log^2 (1/\delta), k))$.     

Design of low‐order controllers satisfying sensitivity constraints for unstructured uncertain plants

This paper presents a simple analytically based algorithm for the design of reduced‐order controllers satisfying frequency‐dependent sensitivity specifications for SISO plants having unstructured uncertainty. The uncertainties can be additive as well as multiplicative, and can take the form of circles, polygons or sectors located around a nominal plant. Moreover, the circle radius and polygon and sector sizes may depend on the frequency. The proposed method is applicable to both continuous and discrete designs. Copyright © 2004 John Wiley & Sons, Ltd.     

Approximate Guarding of Monotone and Rectilinear Polygons

We show that vertex guarding a monotone polygon is NP-hard and construct a constant factor approximation algorithm for interior guarding monotone polygons. Using this algorithm we obtain an approximation algorithm for interior guarding rectilinear polygons that has an approximation factor independent of the number of vertices of the polygon. If the size of the smallest interior guard cover is OPT for a rectilinear polygon, our algorithm produces a guard set of size O(OPT ²).     

平面散乱点集约束Delaunay三角形剖分切割算法

文章提出了一种基于切割的平面散乱点集约束Delaunay三角剖分算法。该算法的基本思路是首先对平面散乱点集作约束最大空圆凸多边形剖分,然后对多边形的内部再作约束Delaunay三角形剖分。文章还证明了平面散乱点集的约束最大空圆凸多边形剖分是唯一的以及约束Delaunay三角剖分的不唯一性仅仅体现在约束最大空圆凸多边形的内部。使用约束最大空圆凸多边形的概念消除了由于“退化”现象（三个以上的点共圆）带来的算法上的潜在错误。     

On approximation behavior of the greedy triangulation for convex polygons

We prove that the greedy triangulation heuristic for minimum weight triangulation of convex polygons yields solutions within a constant factor from the optimum. For interesting classes of convex polygons, we derive small upper bounds on the constant approximation factor. Our results contrast with Kirkpatrick's Ω(n) bound on the approximation factor of the Delaunay triangulation heuristic for minimum weight triangulation of convexn-vertex polygons. On the other hand, we present a straightforward implementation of the greedy triangulation heuristic for ann-vertex convex point set or a convex polygon takingO(n ²) time andO(n) space. To derive the latter result, we show that given a convex polygonP, one can find for all verticesv ofP a shortest diagonal ofP incident tov in linear time. Finally, we observe that the greedy triangulation for convex polygons having so-called semicircular property can be constructed in timeO(n logn).     

无线传感器网络中一种改进的凸规划定位算法

本文以无线传感器网络中的凸规划(Convex)定位算法为研究对象,针对传统凸规划算法引入无效区域导致定位精度不高的问题,提出了一种改进定位算法Convex-CIS(Circle In Shadow)。Convex-CIS算法在传统凸规划算法基础上,在不增加节点开销和硬件设施的情况下,以多边形的最大内接圆圆心作为定位结果,减少影响定位精度的无效区域,进而降低未知节点的定位误差。仿真表明,Convex-CIS算法能有效提高无线传感器网络中未知节点的定位精度。