模糊神经网络理论研究综述

本文对于近年来受到普遍重视的前向模糊神经网络及有反馈的模糊神经网络的性质、学习算法及应用等方面的研究进行了较为详尽的综述，分析了所取得的主要成果及其特点，并指出了今后模糊神经网络理论研究中有待解决的许多问题。     

模糊ART神经网络在运动目标识别中的应用

本文在讨论模糊ＡＲＴ神经网络及其算法的基础上，研究和提出了一种三维运动目标识别方法，利用模糊ＡＲＴ神经网络对运动目标的目标侧面图形进行学习和模式识别。模拟实验表明了该方法的有效性。     

一种基于神经元的自适应模糊推理网络

本文根据Ｔ－Ｓ模糊模型提出了一种新的基于神经元的自适应模糊推理网络，给出了连接结构和学习算法，它能自动学习和修正隶属函数及模糊规则，将其用于Ｂｏｘ的煤气炉，太阳黑子预报以及降雨量预报等不同类型的复杂系统建模，仿真结果表明，该模糊神经网络具有收敛速度快，辨识精度高，泛化能力强和适应范围广等特点，可当作复杂系统建模的一种有效工具。     

特征向量计算的神经网络方法

矩阵特征向量计算在实际问题中有着广泛应用，本文采用神经网络计算方法来研究主元分析（ＰＣＡ）和次元分析（ＭＣＡ）问题．我们首先考虑神经元的情况（ｐ＝１），给出了求矩阵最大特征元和最小特征元的算法。然后对多神经元性形（ｐ〉１），给出了抽取矩阵主元和次元的算法．和目前许多元知的算法不一样，在我们ＰＣＡ的算法中发迹矩阵的负号就能够得到ＭＣＡ问题的解。     

一种求线性预测系数的神经网络方法

本文把神经网络中的Hebbian规则用于线性预测的分析中，得到了一种求解线性预测系数（LPC）的随机近似算法，并完成了对这种算法的严格证明。     

神经网络与模糊逻辑

本文把神经网络模型理论分为四个部分:①神经元模型及其理论;②单层神经网络;③多层神经网络;④模糊神经网络。并分析了一些重要的神经网络模型的结构、算法及其性能。在此基础上,本文还着重分析了神经网络与模糊逻辑的关系,并指出了它们对新一代计算机的研制有着重要的影响。     

企业财务危机预警Rough-Fuzzy-ANN模型的建立及应用

本文提出了一种基于粗糙一模糊神经网络（Rough-Fuzzy-ANN）的企业财务危机建模和预测新方法，并给出了相应的算法，在通过以我国上市公司财务数据为基础进行的实证分析之后，结果表明，Fuzzy-Rough-ANN模型具有预测精度高。学习和泛化能力强，适应性广的优点；同时有效、可行，为企业财务危机的动态预警提供了一条新的途径。     

模糊自组织特征映射模型

本文提出了一种模糊自组织特征映射模型算法，它将模糊ｃ－均值模型结合到Ｋｏｈｏｎｅｎ自组织算法的学习和更新策略中，从而将神经元的侧抑制作用与模糊控制策略有机地结合起来；不仅实现了关于模糊ｃ－均值的优化问题，而且还通过隶属函数的重新构造最终构成了自组织有序拓扑图。仿真结果表明收敛性得到了很大提高。     

遗传神经网络及其在蛋白质二级结构预测中的应用

本文从两个方面对传统的神经网络预测蛋白质二级结构的模型进行改进：一是从算法入手，结合遗传算法，形成遗传神经网络，努力使迭代朝全局最优的方向进行；二是从神经网络的输入层着手，添加反映残基和预测中心位置距离的单元。结果表明，改进的模型对螺旋预测正确率有很大的提高，从L.Howard Holley等人的59．20％到68．67％。     

混沌粒子群神经网络在上证指数预测中的应用

上证指数预测是一个非常复杂的非线性问题,为了提高对上证指数预测的准确性,本文采用基于混沌粒子群(CPSO)算法对BP神经网络算法改进的方法来进行预测.BP神经网络算法目前已经应用到预测、聚类、分类等许多领域,取得了不少的成果.但自身也有明显的缺点,比如易陷入局部极小值、收敛速度慢等.用混沌粒子群算法改进BP神经网络算法的基本思想是用混沌粒子群算法优化BP神经网络算法的权值和阈值,在粒子群算法中加入混沌元素,提高粒子群算法的全局搜索能力.对上证指数预测的结果表明改进后的预测方法,具有更好的准确性.     

A Randomized Algorithm for Triangulating a Simple Polygon in Linear Time

We describe a randomized algorithm for computing the trapezoidal decomposition of a simple polygon. Its expected running time is linear in the size of the polygon. By a well-known and simple linear time reduction, this implies a linear time algorithm for triangulating a simple polygon. Our algorithm is considerably simpler than Chazelle's [3] celebrated optimal deterministic algorithm. The new algorithm can be viewed as a combination of Chazelle's algorithm and of simple nonoptimal randomized algorithms due to Clarkson et al. [6], [7], [9] and to Seidel [20]. As in Chazelle's algorithm, it is indispensable to include a bottom-up preprocessing phase, in addition to the actual top-down construction. An essential new idea is the use of random sampling on subchains of the initial polygonal chain, rather than on individual edges as is normally done. Received April 18, 2000, and in revised form December 7, 2000. Online publication June 20, 2001.     

An effective hybrid algorithm for computing symbolic determinants

A hybrid algorithm for computing the determinant of a matrix whose entries are polynomials is presented. It is based on the dimension-decreasing algorithm [22] and the parallel algorithm for computing a symbolic determinant of [19]. First, through the dimension-decreasing algorithm, a given multivariate matrix can be converted to a bivariate matrix. Then, the parallel algorithm can be applied to effectively compute the determinant of the bivariate matrix. Experimental results show that the new algorithm can not only reduce enormously the intermediate expression swell in the process of symbolic computation, but also achieve higher degree of parallelism, compared with the single parallel algorithm given in [19].     

A practical algorithm for faster matrix multiplication

The purpose of this paper is to present an algorithm for matrix multiplication based on a formula discovered by Pan [7]. For matrices of order up to 10 000, the nearly optimum tuning of the algorithm results in a rather clear non‐recursive one‐ or two‐level structure with the operation count comparable to that of the Strassen algorithm [9]. The algorithm takes less workspace and has better numerical stability as compared to the Strassen algorithm, especially in Winograd's modification [2]. Moreover, its clearer and more flexible structure is potentially more suitable for efficient implementation on modern supercomputers. Copyright © 1999 John Wiley & Sons, Ltd.     

A NONMONOTONE TRUST REGION ALGORITHM FOR NONLINEAR OPTIMIZATION SUBJECT TO GENERAL CONSTRAINTS

In this paper we present a nonmonotone trust region algorithm for general nonlinear constrained optimization problems. The main idea of this paper is to combine Yuan's technique[1] with a nonmonotone method similar to Ke and Han [2]. This new algorithm may not only keep the robust properties of the algorithm given by Yuan, but also have some advantages led by the nonmonotone technique. Under very mild conditions, global convergence for the algorithm is given. Numerical experiments demonstrate the efficiency of the algorithm.     

关于一种循环类预条件方程组的快速求解

１引言考虑下列Ｎ阶线性方程组其中Ｃ１＝,Ｃ２＝０≤ｉ,ｊ≤Ｎ－１,是Ｎ阶循环矩阵,Ｊ１＝（Ｊ）是Ｎ阶置换矩阵,其元素分别满足１９９３年,Ｔ,Ｋ．Ｋｕ,Ｃ．Ｃ．Ｊ．Ｋｕｏ在［１］中取Ｃ１,Ｃ２为实对称循环矩阵,而Ｃ１＋Ｊ１Ｃ２作为预条件矩阵来求解在数字信号处理中有一定应用的Ｔｏｅｐｌｉｔｚ加Ｈａｎｋｅｌ线性方程组［２］,得到了一种高效的预处理其轭梯度算法．当Ｔｏｅｅｌｉｔｚ与Ｈａｎｋｅｌ矩阵之和为正定矩阵且条件数适中时,所需运算量可达到０（Ｎｌｏｇ２Ｎ）,比原有算法［２,３,４］的运算量０（Ｎ２）…     

一个新的BFGS信赖域算法

本文对于无约束最优化问题提出了一个新的BFGS信赖域算法.利用BFGS方法和信赖域方法,提出了改进的BFGS信赖域方法.推广了文献[3,5]中的两种算法,得到一个新的BFGS信赖域算法,在适当条件下证明了算法的全局收敛性.     

一个等式约束问题的拟Newton—信赖域型方法及其收敛性

在[1]中,Vardi提出一个信赖域方法,而收敛性证明却是在精确λ-搜索下给出的,本文在[1]的基础上提出一个新的算法-拟Newton-信赖域型算法,并证明该算法是全局收敛的,通过利用二阶修正技术去修正该算法,我们证明了该算法是局部超线性收敛的。     

Further Developments in an Iterative Projection and Contraction Method for Linear Programming

A linear programming problem can be translated into an equivalent general linear complementarity problem, which can be solved by an iterative projection and contraction (PC) method [6]. The PC method requires only two matrix-vector multiplications at each iteration and the efficiency in practice usually depends on the sparsity of the constraint-matrix. The prime PC algorithm in [6] is globally convergent; however, no statement can be made about the rate of convergence. Although a variant of the PC algorithm with constant step-size for linear programming [7] has a linear speed of convergence, it converges much slower in practice than the prime method [6]. In this paper, we develop a new step-size rule for the PC algorithm for linear programming such that the resulting algorithm is globally linearly convergent. We present some numerical experiments to indicate that it also works better in practice than the prime algorithm.     

A parallel projection method for solving generalized linear least-squares problems

Summary A parallel projection algorithm is proposed to solve the generalized linear least-squares problem: find a vector to minimize the 2-norm distance from its image under an affine mapping to a closed convex cone. In each iteration of the algorithm the problem is decomposed into several independent small problems of finding projections onto subspaces, which are simple and can be tackled parallelly. The algorithm can be viewed as a dual version of the algorithm proposed by Han and Lou [8]. For the special problem under consideration, stronger convergence results are established. The algorithm is also related to the block iterative methods of Elfving [6], Dennis and Steihaug [5], and the primal-dual method of Springarn [14].This material is based on work supported in part by the National Science foundation under Grant DMS-8602416 and by the Center for Supercomputing Research and Development, University of Illinois at Urbana-Champaign     

A Nonmonotone Trust Region Algorithm for Nonlinear Optimization Subject to General Constraints

In this paperwe present a nonmonotone trust region algorthm for general nonlinear constrained optimization problems.The main idea of this paper is to combine Yuan‘‘‘‘s technique[1]with a nonmonotone method similar to Ke and Han[2].This new algorithm may not only keep the robust properties of the algorithm given by Yuan,but also have some advantages led by the nonmonotone technique.Under very mild conditions,global convergence for the algorithm is given.Numerical experiments demostrate the efficency of the algorithm.