Markov链的乘性Schwarz迭代

Multiplicative Schwarz Method for Solving Markov Chains

近来,Marek等将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,研究了Markov链乘性Schwarz迭代的半收敛性,两水平乘性Schwarz迭代的半收敛性和它们的单调性,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 I. Marek,and it is the first time that Markov chains problems are studied in that context. But it is strict to splitting matrix and iterative matrix. 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 multiplicative schwarz iterative method, and hybrid II Schwarz iterative method, the monotone convergence of the multiplicative schwarz iterative method.