随机系数线性方程组正解的一种数值解法  

One kind of Numerical Solution of Positive Solution of Stochastic Coefficient Linear Equations

作　　者：金琦[1] 许世蒙[1] 宋明福[2] 钱坤[1] 

机构地区：[1]装甲兵工程学院基础部,北京100072 [2]装甲兵工程学院装备再制造工程系,北京100072

出　　处：《数学的实践与认识》2009年第1期78-83,共6页Mathematics in Practice and Theory

摘　　要：通过建立摩擦片磨损量的数学模型,引出了随机系数线性方程组的求解问题以及对其解的统计分布上的分析,给出了一个相关定理,阐明了其分布是对称分布,且其正分量出现的概率大于零,从而为讨论此类方程组解的问题提供了统计分析的依据.同时,还利用优化思想对该随机系数线性方程组的正解加以讨论,给出在简约梯度法下正解数值近似解的算例.Establishing mathematical model of friction sheet＇s wear volume, this paper draws out solution problem of stochastic coefficient linear equations. Through analyzing its solution＇s statistical distribution, a relative theorem is given, which expounds that its distribution is the symmetrical distribution and its positive component appearing probability is bigger than zero. Thus for discussing this class of equations＇ solution problem provides statistical analysis basis. At the same time, using optimized thought discusses positive solution of the stochastic coefficient linear equations. Under the reductive gradient method, an example of numerical approximate solution of the positive solution is given.

关 键 词：随机系数 对称分布 正解 优化数值解 简约梯度法 

分 类 号：O241.6[理学—计算数学] O212.1[理学—数学]