论文标题
M/g/1型马尔可夫链的快速固定点迭代的家族
A family of fast fixed point iterations for M/G/1-type Markov chains
论文作者
论文摘要
We consider the problem of computing the minimal nonnegative solution $G$ of the nonlinear matrix equation $X=\sum_{i=-1}^\infty A_iX^{i+1}$ where $A_i$, for $i\ge -1$, are nonnegative square matrices such that $\sum_{i=-1}^\infty A_i$ is stochastic.该方程在分析M/G/1型马尔可夫链中至关重要，因为矩阵$ g $提供了概率的措施。引入了$ g $的数值计算的固定点迭代术，其中包括经典迭代。详细的收敛分析证明，新类中的迭代比经典迭代更快。数值实验证实了我们扩展的有效性。
We consider the problem of computing the minimal nonnegative solution $G$ of the nonlinear matrix equation $X=\sum_{i=-1}^\infty A_iX^{i+1}$ where $A_i$, for $i\ge -1$, are nonnegative square matrices such that $\sum_{i=-1}^\infty A_i$ is stochastic. This equation is fundamental in the analysis of M/G/1-type Markov chains, since the matrix $G$ provides probabilistic measures of interest. A new family of fixed point iterations for the numerical computation of $G$, that includes the classical iterations, is introduced. A detailed convergence analysis proves that the iterations in the new class converge faster than the classical iterations. Numerical experiments confirm the effectiveness of our extension.
