Bernstein多项式的快速复合算法

在计算机辅助几何设计中,Bernstein多项式的复合是一个重要的研究课题。目前,实现复合的方法主要有Blossoming算法和优化的Blossoming算法。这类方法虽然是数值稳定的,但是计算量很大,存储空间和程序复杂性方面也要求较高,文中基于多项式插值和符号运算,提出了一种新的复合算法。理论分析表明,新算法不但保持了数值稳定性,而且在计算量,存储空间和程序复杂性方面明显优于已有算法。     

Running Error Analysis of Evaluation Algorithms for Bivariate Polynomials in Barycentric Bernstein Form

Running error analysis for the bivariate de Casteljau algorithm and the VS algorithm is performed. Theoretical results joint with numerical experiments show the better stability properties of the de Casteljau algorithm for the evaluation of bivariate polynomials defined on a triangle in spite of the lower complexity of the VS algorithm. The sharpness of our running error bounds is shown.     

Application of Symbolic Approach to the Bernstein Expansion for Program Analysis and Optimization

Mathematical packages for static analysis of programs have recently been developed. Although these packages are widely used, they have a number of limitations. In particular, they do not support multivariate polynomials with integer coefficients, which are often met in programs and used for the analysis of systems. Some methods to overcome this difficulty have already been suggested, but, unfortunately, they can be applied to only a subclass of such expressions. In this paper, we suggest a more general approach based on the Bernstein expansion, which facilitates the analysis of integer multivariate polynomials.     

快速分解模拟退火算法在全局查询优化中的应用

文章提出了一种基于快速分解模拟退火算法的全局查询优化算法。快速分解模拟退火算法是一种改进的模拟退火算法,它退火时间短,收敛速度快,磁盘I/O开销小。仿真结果表明,该算法在数据集成系统环境中,无论参与查询的关系数目多少,均有较好的查询优化性能。     

光线寻优算法在函数优化中的应用

光线寻优算法是一种模拟光传播过程的智能优化算法,具有可调参数少、结构简单、容易实现等优点.该算法用网格划分可行域,将具有不同折射率的介质填充到各网格中,并将光在此变折射率介质中的传播路径设想成算法的寻优路径,从而达到自动搜索寻优的目的,将光线寻优算法用于求解文献中的6个标准测试函数,并与模拟退火算法、保留精英遗传算法、...     

Modeling Function Domain for Curves Constructed Based on a Linear Combination of Basis Bernstein Polynomials

Programming and Computer Software - The paper is devoted to designing an automated algorithm for modeling the function domain of spline curves that is needed for developing tools for R-functional...     

球隙迁移算法实现全局优化

给出一种新的优化算法:球隙迁移法.该方法不是已有方法的融合或改进,它利用搜索过程中积累的极小点分布信息形成球隙,以此启发、指导后来的搜索区域,不但逃离了当前局部极小,还能有效地避免重复历史上的多个局部极小.目前的智能算法中,勘探和开采行为相耦合,球隙法实现了勘探与开采的分离,避免了相互干扰,减小了代价,对变量耦合对象的优化效果好.文中证明了球隙法能在有限计算次数内确定地找到连续函数的全局最优.     

带权Bernstein基的对偶基函数在等距逼近中的应用

利用带权Bernstein基的对偶基函数,给出了Bernstein基的对偶泛函和平方可积函数的最小二乘逼近算法,并考虑了满足端点高阶约束条件时的情形.将该算法应用于Bézier曲线等距曲线多项式逼近算法中,不仅可以获得显式的同阶Bézier逼近曲线,还可以满足端点高阶约束条件,进一步还可得到有理逼近算法.数值实例以及与...     

Models for Global Constraint Applications

In this paper we give an overview of some industrial applications built using global constraints. We look at three systems from different application domains and show the core models used to express their constraints. We also consider different search strategies that have been applied and discuss some of the application aspects.     

Formalization of Certain Concepts Related to Experiments

The solution of many problems can be outlined as follows. The investigator possesses a certain basic hypothesis about the properties of the object under investigation; by carrying out experiments with this object, the hypothesis is gradually narrowed down until finally (if the experiment is successful) a definite conclusion is reached.     

Bernstein Bezoutians and application to intersection problems

We study the Bézier curve-surface and Bézier surface-surface intersection problems avoiding the well-known unstable conversion between the Bernstein basis and the power basis. These varieties are given by parameterizations in Bernstein bases and all intermediate computations are performed in that form. For this purpose we construct an adapted resultant for generic Bernstein polynomial systems with a special shape which appear in the intersection problems. This construction is based on the expression of the Bezoutian matrix in Bernstein form.     

粒子群优化算法在神经网络控制中的应用

考虑粒子群优化算法在不确定系统的自适应控制中的应用。神经网络在不确定系统的自适应控制中起着重要作用。但传统的梯度下降法训练神经网络时收敛速度慢,容易陷入局部极小,且对网络的初始权值等参数极为敏感。为了克服这些缺点,提出了一种基于粒子群算法优化的RBF神经网络整定PID的控制策略。首先,根据粒子群算法的基本原理提出了优化得到RBF神经网络输出权、节点中心和节点基宽参数的初值的算法。其次,再利用梯度下降法对控制器参数进一步调节。将传统的神经网络控制与基于粒子群优化的神经网络控制进行了对比,结果表明,后者有更好逼近精度。以PID控制器参数整定为例,对一类非线性控制系统进行了仿真。仿真结果表明基于粒子群优化的神经网络控制具有较强的鲁棒性和自适应能力。     

混沌免疫进化算法及其在函数优化中的应用

基于免疫系统的克隆选择机理,并利用混沌序列的遍历性,提出一种混沌免疫进化算法.算法首先将混沌序列引入算法初始群体的产生和抗体的扩展过程.其次将待扩展群体中的个体亲和度进行变换以调节个体的选择概率.最后利用概率分析方法,给出算法的全局收敛性证明.为了验证算法的有效性,将算法应用于函数优化问题.用不同的测试函数进行仿真实验.仿真结果表明该算法具有不易陷入局部最优、解的精度高、收敛速度快等优点.     

Formalization of Time and Space

Time and space limitations can be specified, and proven, in exactly the same way as functionality. Proofs of time bounds, both implementation-independent and real-time, and of space requirements, both worst-case and average-case, are given in complete detail. Received May 1997 / Accepted in revised form July 1998     

应用罚函数求解二层线性优化问题的全局优化方法

应用罚函数原理，将二层线性优化问题转化为目标函数带有罚函数子项的非线性优化问题，当罚系数大于某一数值时，库函数项为一精确项，该非线性优化问题用渐的进外逼近算法可求出其全局最优解。     

Real-Time Global Illumination for VR Applications

Real-time global illumination in VR systems enhances scene realism by incorporating soft shadows, reflections of objects in the scene, and color bleeding. The Virtual Light Field (VLF) method enables real-time global illumination rendering in VR. The VLF has been integrated with the Extreme VR system for real-time GPU-based rendering in a Cave Automatic Virtual Environment.     

How to Guarantee Finite Termination of Verifying Global Optimization Codes

Convergence or finite termination of algorithms for solving problems of numerical analysis usually is shown only for their original theoretical versions, assuming that all operations appearing in the algorithms can be performed exactly.But in most cases the theoretical version of an algorithm cannot be realized on a computer and it is one of the main tasks of numerical mathematicians to find codeable versions of algorithms sharing the essential properties with their originals.The main problem is, that in any coded version at most rounded approximations of the operations appearing in the theoretical algorithm can be used, and that these approximations are defined only for the finite set of floating point numbers.So e.g. in codes for global optimization only rounded bisection is possible, and even this only finitely often in a meaningful way. In addition there are also problems with controlling rounding errors if underflow or graduated underflow might appear. These problems are often overlooked, even in codes for verifying global optimization.But it is possible to solve these problems by a simple but quite general implementable procedure, guaranteeing that a very natural stopping criterion is satisfied after finitely many steps.     

VB应用程序的速度优化方法

运行速度是衡量应用程序性能的主要因素,VB作为一个可视化的应用程序开发工具,目前得到广泛应用,文中介绍了VB应用程序运行速度的各种优化方法。     

基于B语言的UML形式化方法

分析了目前主要的UML形式化方法及特点,提出了基于B语言的转换方法B2F(B-Based Formalization),通过将UML模型转化为B抽象机描述实现UML的形式化描述和验证,并详细分析了基于B2F方法的UML类图的形式化,证明了该方法的可行性。