随机系数线性方程组的正解问题

Positive Solution Problem of Stochastic Coefficient Linear Equations

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。通过分析其解的统计分布，给出了一个相关定理，阐明了解的分布为对称分布，且其负分量出现的概率大于零。利用优化思想，给出了在信赖域法下求数值化正解的近似解的算例。

In this paper, by establishing mathematical model of friction sheet＇ s wear volume, the authors draw out solution problem of stochastic coefficient linear equations. By analyzing the solution＇ s statistical distribution, this paper gives a relative theorem, which expounds that its distribution is the symmetrical distribution and the occurrence probability of the negative component is bigger than zero. Under the trust region method and by using optimized thought this paper gives an example of approximate solution of the numerical positive solution.