On Finding the Smallest Generalized Eigenpair Using Markov Chain Monte Carlo Algorithm

Farshid Mehrdoust

Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.

DOI: 10.4236/am.2012.36092                

Abstract

This paper proposes a new technique based on inverse Markov chain Monte Carlo algorithm for finding the smallest generalized eigenpair of the large scale matrices. Some numerical examples show that the proposed method is efficient.

Keywords

Monte Carlo Method; Markov Chain; Generalized Eigenpair; Inverse Monte Carlo Algorithm

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	R. Y. Rubinstein, “Simulation and the Monte Carlo Method,” John Wiley & Sons, New York, 1981. doi:10.1002/9780470316511
[2]	Y. Saad, “Numerical Methods for Large Eigenvalue Problems,” Manchester University Press, Manchester, 1991.
[3]	I. Dimov and A. Karaivanova, “Iterative Monte Carlo Algorithm for Linear Algebra Problem,” Lecture Note in Computer Science, 1996.
[4]	I. Dimov, “Monte Carlo Methods for Applied Scientists,” World Scientific Pub., Singapore City, 2008.
[5]	B. Fathi and F. Mehrdoust, “Partitioning Inverse Monte Carlo Iterative Algorithm for Finding the Three Smallest Eigenpairs of Generalized Eigenvalue Problem,” Advances in Numerical Analysis, Vol. 2011, 2011, Article ID: 826376.