Estimating the spectral radius of a real matrix by discrete Lyapunov equation

Abstract

For any real matrix A, this paper is concerned with the estimation of the spectral radius of A. The relationship between the weighted norm and the discrete Lyapunov equation of the matrix A is obtained. On the basis of the relationship, an iterative algorithm is presented to obtain the spectral radius of A and to estimate the solution of the corresponding linear discrete system. Several numerical examples are given to show that the iterative algorithm is effective.

Keywords:

• spectral radius
• estimation of solution
• discrete Lyapunov equation
• linear difference equation

AMS Subject Classification::

• 65F10
• 65F15

Acknowledgements

This work was Supported by the National Natural Science Foundation of China (60872046) and the Key Discipline Development Program of Beijing Municipal Commission (XK100080537).