TY - GEN

T1 - Information theoretic approach to the perron root of nonnegative irreducible matrices

AU - Stańczak, Sławomir

AU - Boche, Holger

PY - 2004

Y1 - 2004

N2 - This paper characterizes the Perron root of nonnegative irreducible matrices in terms of the Kullback Leibler distance (generalized to positive discrete measures). By Perron-Frobenius theory, the Perron root of any nonnegative irreducible matrix is equal to its spectral radius. Thus, the paper establishes a connection between two fundamental concepts of information theory and linear algebra. Moreover, these results are shown to have interesting applications to the classical power control problem in wireless communications networks. Finally, we prove new saddle point characterizations of the Perron root and present possible extensions of the results to more general functions.

AB - This paper characterizes the Perron root of nonnegative irreducible matrices in terms of the Kullback Leibler distance (generalized to positive discrete measures). By Perron-Frobenius theory, the Perron root of any nonnegative irreducible matrix is equal to its spectral radius. Thus, the paper establishes a connection between two fundamental concepts of information theory and linear algebra. Moreover, these results are shown to have interesting applications to the classical power control problem in wireless communications networks. Finally, we prove new saddle point characterizations of the Perron root and present possible extensions of the results to more general functions.

UR - http://www.scopus.com/inward/record.url?scp=19544386434&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:19544386434

SN - 0780387201

T3 - 2004 IEEE Information Theory Workshop - Proceedings, ITW

SP - 254

EP - 259

BT - 2004 IEEE Information Theory Workshop - Proceedings, ITW

T2 - 2004 IEEE Information Theory Workshop - Proceedings, ITW

Y2 - 24 October 2004 through 29 October 2004

ER -