New hybrid Monte Carlo methods and computing the dominant generalized eigenvalue

Abstract

In this paper, the computation of dominant generalized eigenvalue problem using the new Monte Carlo method are presented. We also compare the numerical results and the CPU-time of two different methods for evaluating dominant generalized eigenvalue. The first method is the QR method. The second method is the extended Monte Carlo method which is called the resolvent Monte Carlo algorithm. Finally, using these methods the numerical results for the general symmetric dense/sparse matrices are performed.

Keywords:

• Monte Carlo method
• generalized eigenvalue problem
• Markov chain
• resolvent matrix
• QR method

2000 AMS Subject Classifications :

• 65C05
• 35P15
• 34L16

Notes

The numerical test are performed on Intel(R) (Core(TM)2 CPU, 1.83 GHz) personal machine and MATLAB software 7.6(R2008a).

In these matrices each row is obtained from the previous one by cyclically permuting the entries one step forward.