偏最小二乘回归方法的局限性及改进算法

提出了偏最小二乘回归中的一类不适用情况,并从理论上分析,实例上验证,给出了针对这种情况的一种改进算法,从而拓宽了偏最小二乘回归的使用范围.     

On the Convergence of Backward Differentiation Formulas for Stiff Initial Value Problems

The influence of a time-dependent transformation to a numerical method is studied. Thus convergence results of backward differentiation formulas applied to the non-autonomous stiff system y = A(t)y + (t) are given. The approach is based on a special decomposition of the companion matrix.This revised version was published online in October 2005 with corrections to the Cover Date.     

The least square values and the shapley value for cooperative TU games

The main result proved in this paper is the fact that any Least Square Value is the Shapley value of a game obtained from the given game by rescaling. An Average per capita formula for Least Square Values, similar to the formula for the Shapley value (Dragan (1992)), will lead to this conclusion and allow a parallel computation for these values. The potential for the Least Square Values, a potential basis relative to Least Square Values and an approach similar to the one used for the Shapley value is allowing us to solve the Inverse problem for Least Square Values.     

我国居民年人均收入与消费支出宏观分析与预测

用logistic曲线方程模拟我国居民人均收入、消费支出变化情况,并用该模型对其作短期预测,同时用该模型对居民收入和消费支出变化状况作出了阶段分析,进一步为经济发展作宏观分析和预测提供信息和根据。     

On the Inequalities for Traces and Singular Values of the Quaternion Matrices

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矩阵的特征根与特征向量及其相似对角形的优化求法

研究了矩阵的特征根与特征向量及其相似对角形的优化求法.优化了文[1]的方法,只要对矩阵A的特征矩阵λE-A施行初等变换化为对角形,即可同时求出A的特征根与特征向量,判断A是否可对角化.在A可对角化时,可直接写出相应的可逆矩阵T,使T~(-1)AT为对角形矩阵.     

矩阵的特征根与特征向量及其相似对角形的统一求法

给出了解决矩阵对角化问题的一个简便方法.应用这个方法,可同时求出A的特征根及特征向量,判断A是否可对角化,在A可对角化时,可直接写出相应的可逆矩阵T,使T-1AT为对角形矩阵.