An Extension of Two Conjugate Direction Methods to Markov Chain Problems

Authors

  • Chun Wen University of Electronic Science and Technology of China, School of Mathematical Sciences, 611731, Chengdu, Sichuan
  • Ting-Zhu Huang University of Electronic Science and Technology of China, School of Mathematical Sciences, 611731, Chengdu, Sichuan
  • Tomohiro Sogabe Aichi Prefectural University, Department of Information Science and Technology, Aichi 480-1198

Keywords:

Krylov subspace methods, conjugate direction methods, Markov break chains, stationary probability distribution

Abstract

Motivated by the recent 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. Comput. Appl. Math., Vol. 266, 2009, pp. 103--113], this paper describes two conjugate direction methods, BiCR and BiCG, and attempts to extend their applications to compute the stationary probability distribution for an irreducible Markov chain with the aim of finding an alternative basic solver. Numerical experiments show the feasibility of the BiCR and BiCG to some extent, with applications to several practical Markov chain problems.

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How to Cite

Wen, C., Huang, T.-Z., & Sogabe, T. (2015). An Extension of Two Conjugate Direction Methods to Markov Chain Problems. COMPUTING AND INFORMATICS, 34(2), 495–516. Retrieved from https://www.cai.sk/ojs/index.php/cai/article/view/3211

Issue

Vol. 34 No. 2 (2015): Computing and Informatics

Section

Articles