An Extension of Two Conjugate Direction Methods to Markov Chain Problems
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
Computing and Informatics, Tome 33 (2015) no. 3, / Harvested from Computing and Informatics
Text on Computing and Informatics
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.
Publié le : 2015-10-19
Classification:  Krylov subspace methods, conjugate direction methods, Markov break chains, stationary probability distribution,  60J22, 65C40 
@article{cai3211,
     author = {Chun Wen; University of Electronic Science and Technology of China, School of Mathematical Sciences, 611731, Chengdu, Sichuan and Ting-Zhu Huang; University of Electronic Science and Technology of China, School of Mathematical Sciences, 611731, Chengdu, Sichuan and Tomohiro Sogabe; Aichi Prefectural University, Department of Information Science and Technology,  Aichi 480-1198},
     title = {An Extension of Two Conjugate Direction Methods to Markov Chain Problems},
     journal = {Computing and Informatics},
     volume = {33},
     number = {3},
     year = {2015},
     language = {en},
     url = {http://dml.mathdoc.fr/item/cai3211}
}

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. An Extension of Two Conjugate Direction Methods to Markov Chain Problems. Computing and Informatics, Tome 33 (2015) no. 3, . http://gdmltest.u-ga.fr/item/cai3211/