IJPAM: Volume 81, No. 2 (2012)
FOR THE PERRON ROOT
School of Information Sciences
FI-33014, University of Tampere
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.
Received: March 29, 2011
AMS Subject Classification: 15A18, 15B48
Key Words and Phrases: eigenvalue bounds, Perron root, nonnegative matrices
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395