Markov链平稳分布的迭代解法

Iterative Methods for Solving the Stationary Distribution of Markov Chains

近来,Marek等第一次将Schwarz方法引入了奇异线性方程组的求解问题.然而,这种方法对于分裂阵和迭代阵的要求过于严格.本文在此基础上,利用Drazin逆给出了拟非负分裂的定义.对Markov链分裂阵的要求由非负型分裂推广到拟非负型分裂,证明了Markov链加性Schwarz迭代,诱导分离及其粗网格校正的半收敛性,扩充了Schwarz迭代方法的理论,使这种方法更具实用性.

Up to now,singular systems are analyzed using Schwarz methods by Marek,and it is the first time that Markov chains problems are studied in that context. In this paper, the author gives the definition of quasi-nonnegative splittings. Splitting matrixs vary from nonnegative splittings to quasi-nonnegative splittings. It is shown that the semiconvergence of the additive Schwarz method, induced splitting and corse grid corrections in the case.