Spectral Radius TR

[Bill Horne]

The following technical report is now available


	   Lower bounds for the spectral radius of a matrix

			      Bill Horne
			NEC Research Institute
			  4 Independence Way
			 Princeton, NJ  08540

		     NECI Technical Report 95-14

In this paper we develop lower bounds for the spectral radius of
symmetric, skew-symmetric, and arbitrary real matrices.  Our approach
utilizes the well-known Leverrier-Faddeev algorithm for calculating
the coefficients of the characteristic polynomial of a matrix in
conjunction with a theorem by Lucas which states that the critical
points of a polynomial lie within the convex hull of its roots.  Our
results generalize and simplify a proof recently published by Tarazaga
for a lower bound on the spectral radius of a symmetric positive
definite matrix.  In addition, we provide new lower bounds for the
spectral radius of skew-symmetric matrices.  We apply these results to
a problem involving the stability of fixed points in recurrent neural
networks.

The report can be obtained from my homepage

	   http://www.neci.nj.nec.com/homepages/horne.html

Or directly at

	     ftp://ftp.nj.nec.com/pub/horne/spectral.ps.Z


-- 
  Bill Horne   Senior Research Associate   Computer Science Division
   NEC Research Institute, 4 Independence Way, Princeton, NJ  08540
 horne at research.nj.nec.com  PHN:  (609) 951-2676  FAX: (609) 951-2482
	   http://www.neci.nj.nec.com/homepages/horne.html