# IJPAM: Volume 81, No. 2 (2012)

EXTENDING THE HALL-PORSCHING BOUNDS
FOR THE PERRON ROOT

Jorma K. Merikoski
School of Information Sciences
FI-33014, University of Tampere
FINLAND

Abstract. Let be nonnegative with Perron root  and row sums , and denote , . We improve the Frobenius bounds by applying them to , where is obtained from the identity matrix  by replacing its certain diagonal entries with a suitably chosen positive number. As a special case, in changing only one entry, we obtain the Hall-Porsching bounds.

AMS Subject Classification: 15A18, 15B48

Key Words and Phrases: eigenvalue bounds, Perron root, nonnegative matrices