关于Ck-连续的保形插值样条函数的一点注记

针对有关Ｃｋ一连续的保形插值样条函数在确定边界导数的条件时可能出现多余的拐点,从而破坏了保形性［１,２］的问题,现提出一种修正方法． 我们采用与［２］相同的记号．对于区间［ａ, ｂ］的一个划分 ：ａ＝ｘ０＜ｘ１＜…＜ｘｎ＝ｂ,在每个节点ｘｉ处给定相应的型值ｙｉ,令 首先要指出,［２］之§５数值算例中的数据有误,β２＝－０．５－４＝－４．５而不是－５．５,与之对应的ｍ２＝ ４ ＋ ０．８９（－４．５）＝－０．００５．即使假定原始数据 β２＝一５．５,ｍ２＝－０．９是正确的,按他的原始方程所画的曲线上仍有两…     

矩形区域上仿射变分不等式的一个直接法

１．引言我们将建立一个求解矩形区域上具Ｚ一阵的仿射交分不等式的直接法．设ＡｅＲｎ×ｎ为给定实矩阵,ｑＲｎ为给定实向量,Ｋ为由ｎ个非空闲区间,即组成的Ｃａｒｔｅｓｉａｎ积．考虑仿射变分不等式：求ｘ＊Ｋ,使１得其中ａ;＜ｂｉ对每个指标ｉ＝１,２,…,ｎ都成立．我们允许ａ;或ｂｉ取无穷大,此时意指题（１）,它可写成如下等价形式（可参见［３］）：ＯＭｘ”．ｏＬ＞０．芳ｘｇ＝ａ。（（Ａｘ”．ｏＬ＜０．开ｘ？＝ｂ。门）【（砌”一ＸＬ＝０．若Ｘ。＜Ｘ了＜ｂ．显然,如果Ｋｉ＝【０,十一（ｉ一１,…,。）,则ＶＩ…     

用插值算子解FIF反问题

１．引言 记区间Ｉ＝［０,１］,Ｎ是某给定的正整数,ｘｊ＝ｊ／Ｎ,ｊ＝０,１,…,Ｎ,又给定实函数Ｙ．令 ｛ Ｌｎ（ｘ）＝ Ｎ ＋ Ｎ, Ｆｎ（ｘ,ｙ）＝ｄｎ－１ｙ＋ｈＹ（Ｌｎ（ｘ））－ｄｎ－１Ｙ（ｘ）ｂｎ＝１,２…．Ｎ．（１,１） 其中 （１）ｈＹ（ｘ）∈Ｃ（Ｉ）,满足插值条件：ｈＹ（ｘｊ）＝Ｙ（ｘｊ）,ｊ＝０,１;…,Ｎ （２）ｂｙ（ｘ）∈Ｃ（Ｉ）,满足条件：ｂＹ（ｘ０）－Ｙ（ｘ０）,ｂＹ（ｘＮ）＝Ｙ（ｘＮ）; （３）实数列｛ｄｉ｝Ｎ－１ｉ＝０满足｜ｄｉ｜＜１,Ｖｉ． 定义 Ｗｕ （ｘ,ｙ）＝（Ｌｎ（ｘ）…     

关于非对称线性方程组的新迭代算法

５１．引言 二阶椭圆型非对称方程是一类重要的科学工程计算的数学模型,如对流扩散和油藏模拟方程等,有着广泛的实际应用背景．文献［２］和［３］基于原始微分方程及对应的离散问题提出了正定可对称化的新概念．基于这一概念及文山我们研究针对二维和三维二阶常系数非对称椭圆型方程数值模型的新选代算法,首先考虑下面的一维椭圆型问题：对区间［０,１］均匀剖分后得ｎ＋２节点,即ｘ;一ｉ·ｈ;ｉ＝０,··,,ｎ＋１,其中ｈ＝／（＋１）．如果用中心差分格式离散方程（１．１）,则在节点Ｘ;有如下差分方程： 一（１＋ｗＮ。;－…     

滞后不确定性系统的鲁棒控制

１主要结果本文将文［１］的结论推广到具有多重状态时滞和多重控制时滞的不确定性系统ｘ（ｔ）＝（Ａ０＋Ｂ０ΔＡ０（ｒ０（ｔ）））ｘ（ｔ）＋∑Ｎｉ＝１Ｂ０（Ａｉ＋ΔＡｉ（ｒｉ（ｔ）））ｘ（ｔ－ｄｘｉ（ｔ））＋（Ｂ０＋Ｂ０ΔＢ０（ｓ０（ｔ）））ｕ（ｔ）＋∑Ｍ...     

一类本身具有预条件功能的ABS型共轭梯度算法

１．引言对于大型线性方程组Ａｘ＝ｂ,其中ＡＥＲｎｘｎ是一个非奇异矩阵,ｘ,ｂＲｎＶｏｙｅｖｏｄｉｎ［７］提出了一类共轭梯度算法．该算法中含有两个作为参数的非奇异矩阵Ｂ;ＣＲｎｘｎ,它们满足关系式ＣＡＢＣ－１＝ａＩ＋βＢＴＡＴ,（１）其中ａβＲ为纯量．设内积（ｘ,ｙ）＝ｙＴｘ为普通数量积,Ｖｏｙｅｖｏｄｉｎ共轭梯度法如下：算法１．步０．设。０为精确解０”的一个初始近似,计算残差,。一＊。。一ｂ．若,。＝０则停止;否则,置Ｓ。＝,。,ｉ二０,转步１．步１．计算。;＋１。;一（,;,＊,Ｊ八,;,＊＊…     

一种快速生成2k3型Hadamard矩阵的算法

１．引言所谓ｈａｄａｍａｒｄ矩阵［１］Ｋｎ是指以１或－１作为元素并满足ＨｎＨＩ＝ｎＩ的ｎ阶方阵．Ｈａｄａｍａｒｄ矩阵在数字图象处理［２］、编码理论［３］、数字通信、多比特扩散码［４、区组设计等领域都有十分出色的应用,在应用中常常用到各阶具体的Ｈａｄａｍａｒｄ矩阵,因此研究如何快速生成各阶Ｈａｄａｍａｒｄ矩阵Ｈｎ是十分必要的．有关Ｈａｄａｍａｒｄ矩阵已有一些结论［１］：定理１．设ｎ＞２,Ｈｎ是Ｈａｄａｍａｒｄ矩阵,则ｎ＝０ｍｏｄ４．定理２．若Ｈｎ是Ｈａｄａｍａｒｄ矩阵,则也是Ｈａｄａｍａｒｄ矩阵．…     

欧拉方程的velicity表示和辛积分(Ⅱ)

１．引言这篇文章的目的是辨别辛方法得出的结果与龙格－库塔法相比是同样好或是更好,特别对长时间．文中的数值实验显示对于ｔ＝０．１,用ＩＭ格式,在ｔ＝６时将得到不均匀分布的点．２．计算的描述本文将显示用［４］中描述的近似获得的数值结果．结论写在末尾．对［４］中的哈密顿系统（２１）,（２２）,本文将对隐式中点格式（ＩＭ）和二级四阶高斯－勒让德龙格－库塔方法与标准四阶龙格－库塔方法作比较．在数值实验中用了三个不同的哈密顿函数：一个是［４］中哈密顿函数（１９）,其他的是通过省略ｋ＝ｊ项和双倍这项从［４］中…     

关于S_4~2(△_(mn)~((2)))插值与逼近

§１．引言及定义 设平面上矩形 Ｄ：［a,b］×［ｃ,ｄ］上的 Ⅱ型三角剖分（图５）．令 ｈ１＝,ｈ２＝．为方便,（ｉ,ｊ）（ｉｈ１,ｊｈ２）．记表示总次数不超过４的二元多项式空间;Ｄｉｊ表示以（ｉ,ｊ）,（ｉ ＋１,ｊ）（ｉ,ｊ＋１）,（ｉ＋１, ｊ＋１）为顶点的矩形,其上的四个三角形域依次记为（ｋ＝１,２,３,４）． 定义 １．１．二元四次样条集S_4～2（△_（mm）～（（２）））是由满足下列条件的Ｓ（ｘ,ｙ）所组成的集合： （ｉ） Ｓ（ｘ,ｙ） Ｃ２（Ｄ）;（ｉｉ）Ｓ（ｘ,ｙ）（ｋ＝１,２,３,４）． 设一…     

关于H∞代数Riccati方程可解性的频率判据和解的Yakubovich算法

１　引言众所周知,在Ｈ∞控制问题的状态空间解法中关键的步骤是判断代数Ｒｉｃｃａｔｉ方程－ＣＴＣ－ＡＴＹ－ＹＡ＋Ｙ（ＢＢＴ－γ－２ＧＧＴ）Ｙ＝０（１）半正定镇定解的存在性并求出该解［１,２］．上式中Ａ,Ｂ,Ｇ,Ｃ为给定的适当维数的实矩阵;γ为一预先未知的正实数,它代表着干扰抑制水平;上标“Ｔ”表示矩阵或向量的转置．目前,虽然有许多方法（如牛顿迭代法、哈米顿矩阵的不变子空间法、广义特征子空间法、矩阵符号函数法等）可用来求解代数Ｒｉｃｃａｔｉ方程,但由于方程（１）中参数γ事先未知,使得应用这些方法时需…     

Evolutionary Algorithms for Minimax Problems in Robust Design

Many robust design problems can be described by minimax optimization problems. Classical techniques for solving these problems have typically been limited to a discrete form of the problem. More recently, evolutionary algorithms, particularly coevolutionary optimization techniques, have been applied to minimax problems. A new method of solving minimax optimization problems using evolutionary algorithms is proposed. The performance of this algorithm is shown to compare favorably with the existing methods on test problems. The performance of the algorithm is demonstrated on a robust pole placement problem and a ship engineering plant design problem.     

Algorithms to solve some classes of network minimax problems and their applications

We consider some classes of network minimax problems that generalize combinatorial versions of shortest and longest path problems in networks. Effective polynomial-time algorithms are proposed for solving these problems.Translated from Kibernetika, No. 1, pp. 70–75, January–February, 1991.     

Robust Nonlinear Model Predictive Control With Variable Block Length

Robust model predictive controllers for discrete-time nonlinear systems are proposed in this technical note. The algorithms first search for an open-loop controller with some block length, and then try to improve it in a closed-loop fashion by solving minimax problems on-line. It is proved that the controllers are capable of making a subsequence of the state converge into a target set in the presence of bounded disturbances.      

No free lunch theorems for optimization

A framework is developed to explore the connection between effective optimization algorithms and the problems they are solving. A number of “no free lunch” (NFL) theorems are presented which establish that for any algorithm, any elevated performance over one class of problems is offset by performance over another class. These theorems result in a geometric interpretation of what it means for an algorithm to be well suited to an optimization problem. Applications of the NFL theorems to information-theoretic aspects of optimization and benchmark measures of performance are also presented. Other issues addressed include time-varying optimization problems and a priori “head-to-head” minimax distinctions between optimization algorithms, distinctions that result despite the NFL theorems' enforcing of a type of uniformity over all algorithms     

Closed Transportation Models with Minimax Criterion

Transportation problems are investigated by replacing the classical transportation cost minimization functionals by minimax functionals. Transportation models with minimax criteria are described and optimization algorithms for them are designed. A formula for computing the minimax matrix (a matrix of the classical transportation polyhedron whose largest element is minimal) of the transportation polyhedron is derived. One of the algorithms generates a (hereditarily minimax) matrix such that every each of its submatrices is a minimax matrix of the transportation polyhedron to which the matrix belongs.     

On Discrete Minimax Problems in R Using Interval Arithmetic

Interval algorithms for bounding discrete minimax function values of problems in which the constituent minimax functions are continuously differentiable functions of one real variable in a bounded closed interval are presented, both with and without inequality constraints represented by continuously differentiable constraint functions.     

Minimax method in optimizing energy consumption in real-time embedded systems

The main principles of the minimax method designed for solving energy consumption optimization problems in real-time embedded systems are presented. Results of comparing ways to minimize energy consumption in systems with on-line minimax and off-line DVS/DFS scheduling are given. In terms of energy consumption minimization, the minimax method is shown to ensure optimal division of the task into two subtasks. This method can be applied both to systems with tasks arbitrarily distributed in time and to periodic multitasking systems with rigid timing constraints.     

Solution of minimax problems using equivalent differentiable functions

A method is proposed for the solution of minimax optimization problems in which the individual functions involved are convex. The method consists of solving a problem with an objective function which is the sum of high powers or strong exponentials of the separate components of the original objective function. The resulting objective function, which is equivalent at the limit to the minimax one, is shown to be smooth as well as convex. Any efficient nonlinear programming method can be utilized for solving the equivalent problem. A number of examples are discussed.     

A stochastic algorithm for makespan minimized multi-agent path planning in discrete space

Makespan minimized multi-agent path planning (MAPP) requires the minimization of the time taken by the slowest agents to reach its destination. The resulting minimax objective function is non-smooth and the search for an optimal solution in MAPP can be intractable. In this work, a maximum entropy function is adopted to approximate the minimax objective function. An iterative algorithm named probabilistic iterative makespan minimization (PIMM) is then proposed to approximate a makespan minimized MAPP solution by solving a sequence of computationally hard MAPP minimization problems with a linear objective function. At each iteration, a novel local search algorithm called probabilistic iterative path coordination (PIPC) is used to find a sufficiently good solution for each MAPP minimization problem. Experimental results from comparative studies with existing MAPP algorithms show that the proposed algorithm strikes a good tradeoff between the quality of the makespan minimized solution and the computational cost incurred.     

一类非线性极小极大问题的改进粒子群算法

针对一类非线性极小极大问题目标函数非光滑的特点给求解带来的困难,利用改进的粒子群算法并结合极大熵函数法给出了此类问题的一种新的有效算法。首先利用极大熵函数将无约束和有约束极小极大问题转化为一个光滑函数的无约束最优化问题,将此光滑函数作为粒子群算法的适应值函数;然后用数学中的外推方法给出一个新的粒子位置更新公式,并应用这个改进的粒子群算法来优化此问题。数值结果表明,该算法收敛快﹑数值稳定性好,是求解非线性极小极大问题的一种有效算法。