计算Hamilton矩阵特征值的一个稳定的有效的保结构的算法

提出了一个稳定的有效的保结构的计算Hamilton矩阵特征值和特征不变子空间的算法,该算法是由SR算法改进变形而得到的。在该算法中,提出了两个策略,一个叫做消失稳策略,另一个称为预处理技术。在消失稳策略中,通过求解减比方程和回溯彻底克服了Bunser Gerstner和Mehrmann提出的SR算法的严重失稳和中断现象的发生,两种策略的实施的代价都非常低。数值算例展示了该算法比其它求解Hamilton矩阵特征问题的算法更有效和可靠。     

一种新的修正SR1更新公式及其算法收敛性

SR1更新公式对比其他的拟牛顿更新公式,会更加简单且每次迭代需要更少的计算量。但是一般SR1更新公式的收敛性质是在一致线性无关这一很强的条件下证明的。基于前人的研究成果,提出了一种新的修正SR1公式,并分别证明了其在一致线性无关和没有一致线性无关这两个条件下的局部收敛性,最后通过数值实验验证了提出的更新公式的有效性,以及所作出假设的合理性。根据实验数据显示,在某些条件下基于所提出更新公式的拟牛顿算法会比基于传统的SR1更新公式的算法收敛效果更好一些。     

一种新的修正SR1更新公式及其算法收敛性

SR1更新公式对比其他的拟牛顿更新公式,会更加简单且每次迭代需要更少的计算量。但是一般SR1更新公式的收敛性质是在一致线性无关这一很强的条件下证明的。基于前人的研究成果,提出了一种新的修正SR1公式,并分别证明了其在一致线性无关和没有一致线性无关这两个条件下的局部收敛性,最后通过数值实验验证了提出的更新公式的有效性,以及所作出假设的合理性。根据实验数据显示,在某些条件下基于所提出更新公式的拟牛顿算法会比基于传统的SR1更新公式的算法收敛效果更好一些。     

基于引力搜索和粒子群混合优化算法的证券投资组合问题研究

本文研究考虑交易成本的投资组合模型,分别以风险价值(VAR)和夏普比率(SR)作为投资组合的风险评价指标和效益评价指标。为有效求解此模型,本文在引力搜索和粒子群算法的基础上提出了一种混合优化算法(IN-GSA-PSO),将粒子群算法的群体最佳位置和个体最佳位置与引力搜索算法的加速度算子有机结合,使混合优化算法充分发挥单一算法的开采能力和探索能力。通过对算法相关参数的合理设置,算法能够达到全局搜索和局部搜索的平衡,快速收敛到模型的最优解。本文选取上证50股2014年下半年126个交易日的数据,运用Matlab软件进行仿真实验,实验结果显示,考虑交易成本的投资组合模型可使投资者得到更高的收益率。研究同时表明,基于PSO和GSA的混合算法在求解投资组合模型时比单一算法具有更好的性能,能够得到满意的优化结果。     

最优化梯度法的改进

本文对最优化方法中的梯度算法进行了改进，使改进后的算法比梯度法的收敛速度快，而且该算法比牛顿法计算量小。     

L—Fuzzy拓扑空间中的可数SR—紧性

从层次结构入手引入L－fuzzy拓扑空间中的可数SR－紧性,证明了可数SR－紧性对强半闭子集遗传,可数SR－紧子集在S－不定映射 像保持,给出了可数SR－紧性的几何刻画与有限交性质的刻画。     

算子RS和SR的局部谱性质

对算子RS和SR的局部谱性质进行了比较系统的研究,得到如下结果:RS具有(C)属性当且仅当SR具有(C)属性;RS具有有限升当且仅当SR具有有限升;RS具有(β)_ε属性当且仅当SR具有(2)_ε属性;RS和SR具有相同的非零Kato谱.     

基于非对称幂分布的中国开放式基金业绩评价和检验

证券投资基金是现代金融业的重要组成部分。随着基金业的迅速发展,证券投资基金已成为我国资本市场最大、最有影响力的机构投资者。目前,开放式基金的数量和规模已远远超过封闭式基金,因此,本文主要探讨开放式基金的业绩评价和排名。已有大量实证研究发现基金收益具有尖峰厚尾性、非对称性和强正相关性,基于此,本文使用非对称幂分布(Asymmetric Power Distribution,APD)来拟合基金收益率分布。不同于其它文献的是,我们主要着眼于Sharpe比率估计量SR,研究36只开放式基金实际日收益率下SR和基于APD标准差和VaR的修正SR,并使用双样本统计量对SR进行假设检验,结论证明了假设检验是显著的,且在基金排名和评价的应用中是非常可行的。     

应用DEKF算法训练模糊化神经网络

模糊MLP网络的待定参数规模比确定性MLP网络的多几倍，急需找到高效的训练算法。本文尝试用DEKF训练模糊神经网络，这是DEKF算法新的应用。仿真表明，DEKF算法比经典BP算法的收敛速度更快，训练所得网络的精度更高。     

线性规划流动等值面算法

对于线性规划问题，本文给出了基于流动等值面的等价模型，提出了一种不可行流动等值面算法．新算法保留了传统单纯形算法的优点并克服了它的不足。初步数值结果表明新算法比传统方法更为有效．     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.     

Towards Excellence in Science Chinese Academy of Sciences

<正>May 26,2014,Beijing Science is a human enterprise in the pursuit of knowledge.The scientific revolution that occurred in the 17th Century initiated the advances of modern science.The scientific knowledge system created by     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

<正>August 10-14,2015Beijing,ChinaThe International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

Bounds for the zeros of polynomials

Let P(z)=∑↓j=0↑n ajx^j be a polynomial of degree n. In this paper we prove a more general result which interalia improves upon the bounds of a class of polynomials. We also prove a result which includes some extensions and generalizations of Enestrǒm-Kakeya theorem.     

Boundedness of commutators related to Marcinkiewicz integrals on hardy type spaces

In this paper, the authors study the boundedness of the operator [μΩ, b], the commutator generated by a function b ∈ Lipβ(Rn)(0 ＜β≤ 1) and the Marcinkiewicz integrals μΩ, on the classical Hardy spaces and the Herz-type Hardy spaces in the case Ω∈ Lipα(Sn-1)(0 ＜α≤ 1).     

Generalization of the interaction between Haar approximation and polynomial operators to higher order methods

In applications it is useful to compute the local average empirical statistics on u. A very simple relation exists when of a function f（u） of an input u from the local averages are given by a Haar approximation. The question is to know if it holds for higher order approximation methods. To do so, it is necessary to use approximate product operators defined over linear approximation spaces. These products are characterized by a Strang and Fix like condition. An explicit construction of these product operators is exhibited for piecewise polynomial functions, using Hermite interpolation. The averaging relation which holds for the Haar approximation is then recovered when the product is defined by a two point Hermite interpolation.     

Jacobi polynomials used to invert the laplace transform

Given the Laplace transform F(s) of a function f(t), we develop a new algorithm to find an approximation to f(t) by the use of the classical Jacobi polynomials. The main contribution of our work is the development of a new and very effective method to determine the coefficients in the finite series expansion that approximation f(t) in terms of Jacobi polynomials. Some numerical examples are illustrated.