论文标题
在马尔可夫链建模中出现的基质方程的松弛固定点迭代
Relaxed Fixed Point Iterations for Matrix Equations Arising in Markov Chains Modeling
论文作者
论文摘要
我们提供了一些固定点迭代的加速变体，用于计算与M/G/1型Markov链相关的单侧矩阵方程的最小非负解。这些变体源自与马尔可夫链相关的Hessenberg M-Matrix的某些楼梯常规分裂。通过利用楼梯配置文件，我们引入了两步的固定点迭代。通过计算连续两个步骤获得的近似值之间的加权平均值，可以进一步加速迭代。证明了基本的两步固定点迭代及其松弛修饰的收敛性。我们的理论分析以及几个数值实验表明，所提出的变体通常优于经典迭代。
We present some accelerated variants of fixed point iterations for computing the minimal non-negative solution of the unilateral matrix equation associated with an M/G/1-type Markov chain. These variants derive from certain staircase regular splittings of the block Hessenberg M-matrix associated with the Markov chain. By exploiting the staircase profile we introduce a two-step fixed point iteration. The iteration can be further accelerated by computing a weighted average between the approximations obtained at two consecutive steps. The convergence of the basic two-step fixed point iteration and of its relaxed modification is proved. Our theoretical analysis, along with several numerical experiments show that the proposed variants generally outperform the classical iterations.
