直接消耗系数矩阵特征值的经济意义研究

基于Leontief提出的投入产出分析和华罗庚的正特征向量法,对直接消耗系数矩阵的特征值进行研究。根据中国多年的实际消耗系数数据计算,得出矩阵特征值具有很好的规律性。根据推广的有消费的华氏开放模型,矩阵特征值的经济含义是它表示一个界限,总投入系数必须大于矩阵的最大正特征值,是保证国民经济总产出不断增长的条件之一。中国的国民经济从1987年开始,到2007年,总产出不断增加的原因之一是因为总投入系数不断增大。     

关于矩阵特征值应用的探索

矩阵的特征值在众多的领域中都存在着非常广泛的应用,能够解决众多的实际问题。因此,矩阵的特征值的应用具有非常重要的意义。本文主要进行了关于矩阵特征值的应用的探索,对于矩阵特征值在数学建模问题方面的应用进行了总结和梳理。     

实三阶矩阵幂收敛于零矩阵的一个充要条件

取消了文献[2]判断实三阶矩阵的幂收敛性的限制条件，给出了实三阶矩阵的幂收敛于零矩阵的一般性判别方法．     

On consequences of one missing observation in a balanced design

It is shown that the C-matrix of a balanced design commutes with the C-matrix of a design resulting from this balanced design because of one missing observation. This commutativity leads us to a simple test procedure for testing equality of treatment effects.     

Sensitivity analysis in maximum likelihood factor analysis

The present paper deals with sensitivity analysis in maximum likelihood factor analysis. To investigate the influence of a small change of data we derive theoretical influence functions I(x; LL^T ) and I(x; Δ) for a common variance matrix T= LL^T and a unique variance matrix Δ respectively. Numerical examples are shown to illustrate our procedure.     

Generating generalized cyclic designs with factorial balance

An algorithm for generating paired comparison factorially balanced generalized cyclic designs is described. The algorithm is based upon the 2 ⁿ ? 1 class association scheme defined by Shah (1960) for n-factor experiments. The algorithm is highly successful in achieving its objective. Firstorder designs with block size greater than two can also be obtained using the algorithm.     

Sensitivity analysis in principal component analysis:influence on the subspace spanned by principal components.

The problem of detecting influential observations in principalcomponent analysis was discussed by several authors. Radhakrishnan and kshirsagar ( 1981 ), Critchley ( 1985 ), jolliffe ( 1986 )among others discussed this topicby using the influence functions I(X;θ_s)and I(X;V_s)of eigenvalues and eigenvectors, which wwere derived under the assumption that the eigenvalues of interest were simple. In this paper we propose the influence functionsI(X;∑^q _s=1θ_sV_sV_s ^T)and I(x;∑^q _s=1V_sV_s ^t)(q<p;p:number of variables) to investigate the influence onthe subspace spanned by principal components. These influence functions are applicable not only to the case where the edigenvalues of interst are all simple but also to the case where there are some multiple eigenvalues among those of interest.     

Jacobi型方法的一些研究

回顾了Jacobi方法与拟-Jacobi方法的发展历史,介绍了并行Jacobi方法与并行拟-Jacobi方法的研究现状.针对网格状分布式多处理机系统就非对称广义特征值问题设计了一种拟-Jacobi方法的并行处理方案,并对G.W.Stewart提出的一种算法做了修正.     

非对称广义特征值问题重特征值的灵敏度分析

以标准特征值问题灵敏度分析的有关结论为基础,证明了单参数非对称广义特征值问题半单重特征值的可微性,给出了特征值导数的表达式和特征向量的级数展开式.以所得结论为基础,定义了广义特征值问题半单重特征值的灵敏度,给出了确定矩阵对中敏感元素的方法.     

关于亚正定矩阵的数值半径

给出了亚(半)正定矩阵数值半径计算的一个方法,该结果与文献[1]结果的使用范围互不包含,给出了其Gerschgorin型简单实用的下界估计式,以及其它有关结果。