逆M矩阵模型的完备及其算法设计

1 引 言 M矩阵是具有非负对角元和非正非对角元且其逆是非负矩阵的一类矩阵.逆M矩阵即逆为M矩阵的一类非负矩阵.逆M矩阵在物理学,生物学,控制理论,神经网络方面有着重要的应用.所以对逆M矩阵的研究一直在持续不断的进行.一个“部分矩阵”是指在一个矩阵中,一些元素已经给定了,而另一些元素待定的矩阵.而一个矩阵的完     

回路图的部分逆M矩阵完备问题

<正>1引言M矩阵是具有非正非对角元且其逆是非负矩阵的一类矩阵.1977年wmoughby~([1])提出把非负矩阵的逆是M矩阵的这一类矩阵定义为逆M矩阵.逆M矩阵在生物学、经济学、智能科学、计算方法等许多科学中都具有重要应用,许多实际问题的结论都可以归结到逆M矩阵的判定上,因此研究逆M矩阵的判定方法,成为当今矩阵理论研究中的一个热点,而利用图论知识研究逆M矩阵完备问题是逆M矩阵研究中的一个重要方     

回路1、2-弦图的逆M矩阵完备及其算法设计

对已定元均不为零的部分逆M矩阵,通过变换使其对角线上元素均为1后,根据其所对应图形的特点,得到结果如下:(a)若其所对应图形为简单有向回路或回路1-弦图,具有逆M矩阵完备式当且仅当所有简单有向回路的回路积均小于1.(b)若其所对应图形为回路2-弦图,具有逆M矩阵完备式当所有简单有向回路满足回路积小于1,且对其中依次在两个顶点处相交的有向回路标明层次后,任一有向回路的回路积均小于与其相连接的上一层的有向回路的回路积.     

非奇异M矩阵的判定及并行算法

1　引　　言M矩阵是一类具有非正非对角元和非负对角元的实方阵 .M矩阵在生物学、经济学、智能科学、计算方法等许多学科中都有重要应用 .许多实际问题的应用都归到 M矩阵的判定上 .例如判定一个矩阵是否为 M矩阵在网络计算中可以判定一个离散动力系统是否稳定 .在数值计算中 ,可以判定一个迭代系统是否收敛 .因此研究 M矩阵的判定方法成为矩阵理论研究中极为活跃的一个领域 .目前国内外许多数学工作者都在研究 M矩阵的判定方法 ,已有的研究成果都是对 M矩阵的整体进行讨论 ,这对高阶矩阵来说 ,不仅计算困难 ,而且需要对判定定理进行消化…     

立方非负的不可约符号模式

以 ，-，0为元素的矩阵称为符号模式矩阵．本文考虑符号模式矩阵的立方模式，给出了至少含一个负元的不可约符号模式的立方模式是非负的充要条件及在置换相似下的标准型；得到了立方非负的符号模式矩阵中出现的正元素的个数的最大(小)值及给出了达到这些最大(小)值的不可约符号模式矩阵的完整刻画．     

非负矩阵最大特征值的新界值

对最大特征值的上下界进行估计是非负矩阵理论的重要部分,借助两个新的矩阵,从而得到一个判定非负矩阵最大特征值范围的界值定理,其结果比有关结论更加精确.     

三对角逆M矩阵的判定

1、引言 三对角逆M矩阵是指同时为三对角矩阵和逆M矩阵的一类特殊矩阵．文用图论方法探讨三对角逆M矩阵结构,给出了三对角矩阵为逆M矩阵的充分必要条件．此条件提供了判定三对角矩阵是逆M矩阵的方法,但较复杂．文讨论了这类矩阵在Hadamard积下的封闭性．由于三对角逆M矩阵在理论和应用上都有一定价值,所以,寻求一种简单而实用的判定方法是必要的．本文通过对这类矩阵结构特点的研究找到了这样一种方法．同时,由此证明了这类矩阵在Hadamard积下的封闭性．     

非负不可约矩阵的广义Perron补矩阵

1989年Meyor为计算马尔可夫链的平稳分布向量构造了一个算法，首次提出非负不可约矩阵的Perron补矩阵的概念，本给出非负不可约矩阵A的广义Perron补矩阵若干性质，并且证明若矩阵A是不可约逆M-矩阵，其广义Perron补矩阵也是不可约逆M-矩阵。     

关于非负不可约矩阵的广义Perron补的一些性质

1989年Meyer为计算马尔可夫链的平稳分布向量构造了一个算法，首次提出非负不可约矩阵的Perron补的概念。本文给出非负不可约矩阵A的广义Perron补若干性质，并且证明当矩阵A是不可约逆M-矩阵，其广义Perron补也是不可约逆M-矩阵。     

有M P逆的Abel范畴中态射方程αxα*=β的非负定解

该文讨论了有M P逆的Abel范畴中态射方程αxα*=β的非负定解和正定解．作为其应用，给出了p 除环上矩阵方程AXA*=B的相关结果     

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.     

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.     

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.     

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     

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     

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).     

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.     

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.