高阶马尔科夫链极限概率分布的一种松弛算法  

A relaxation algorithm for limiting probability distribution of high-order Markov chain

作　　者：宋素华 喻高航 SONG Suhua;YU Gaohang(School of Sciences,Hangzhou Dianzi University,Hangzhou Zhejiang 310018,China)

机构地区：[1]杭州电子科技大学理学院,浙江杭州310018

出　　处：《杭州电子科技大学学报（自然科学版）》2022年第2期90-95,共6页Journal of Hangzhou Dianzi University：Natural Sciences

基　　金：国家自然科学基金资助项目(1207011078)。

摘　　要：针对由高阶马尔科夫链产生的转移概率张量的极限概率分布问题,提出一种松弛算法,可以看成是一种带动量项的高阶幂法。在0<β,γ<1-η_(m)/ 2η_(m)的条件下,算法具有全局收敛性。数值实验表明,通过选取适当松弛参数,所提算法能够有效改善原高阶幂法的计算效率。A relaxation algorithm is proposed to solve the limiting probability distribution problem of the transition probability tensor arising from the higher-order Markov chain,which can be regarded as a higher-order power method with momentum.The convergence analysis is given for the proposed algorithms under the conditions of 0<β,γ<1-η_(m)/ 2η_(m).Numerical experiments show that the proposed algorithm can effectively improve the computational efficiency of the original high-order power method by selecting appropriate relaxation parameters.

关 键 词：马尔科夫链 高阶幂法 张量方程 转移概率张量 极限概率分布向量 

分 类 号：O221.2[理学—运筹学与控制论]