比较应用于马尔科夫链问题的两个共轭方向算法.doc

文档介绍：比较应用于马尔科夫链问题的两个共轭方向
算法
文春,黄廷祝
电子科技大学数学科学学院,成都 611731
摘要:共轭梯度算法可进一步应用于求解非对称线性系统,受文献[An extension of the
conjugate residual method to nonsymmetric linear systems [J]. J. Comput. Appl. Math.,
266:103-113, 2009] 的启发,本文描述了两个共轭梯度算法,即 Bi-CG 和 Bi-CR 算法,并试图
推广到求解不可约马尔科夫链的平稳概率分布. 通过一些实际的马尔科夫链问题,数值实验说
明了 Bi-CG 和 Bi-CR 算法的有效性并做了相应的比较.
关键词:Krylov 子空间方法; 共轭方向算法; 马尔科夫链; 平稳概率分布.
中图分类号: 60J22; 65C40
parison of two conjugate direction
methods, with applications to Markov chains
WEN Chun, HUANG Ting-Zhu
School of Mathematical Sciences/Institute putational Science, University of Electronic
Science and Technology of China, Chengdu 611731
Abstract: Motivated by the celebrated extending applications of the conjugate residual
method to nonsymmetric linear systems by Sogabe, Sugihara and Zhang [An extension of the
conjugate residual method to nonsymmetric linear systems [J]. J. Comput. Appl. Math.,
266:103-113, 2009], this paper describes two conjugate direction methods, Bi-CR and Bi-CG,
and attempts to extend their applications pute the stationary probability distribution
for an irreducible Markov chain. Numerical experiments show the feasibility of the Bi-CR and
Bi-CG methods to some extent, with applications to several practical Markov chain problems.
Key words: Krylov subspace methods; Conjugate direction methods; Markov chains;
Stationary probability distribution.
基金项目: Chinese Universities Specialized Research Fund for the Doctoral Program (201**********).
作者简介: Wen Chun (1986-), female, lecturer, major research direction: puting methods and applications.
Huang Ting-Zhu (1964-), male, professor, major research direction: numerical linear algebra with applications, preconditioning
technologies, and matrix analysis with applications.
-1-
0 Introduction
Krylov subspace methods are one of the most widespread and extensively accepted tech-
niques for numerical solutions of today’s large-scale linear systems of the form
Ax = b,

(1)
where A ∈ Rn×n, x, b