The lower and upper bounds on Perron root of nonnegative irreducible matrices

✍ Scribed by Guang-Xin Huang; Feng Yin; Ke Guo

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 155 KB
• Volume: 217
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2007.06.034

✦ Synopsis

Let A be an n × n nonnegative irreducible matrix, let A[ ] be the principal submatrix of A based on the nonempty ordered subset of {1, 2, . . . , n}, and define the generalized Perron complement of A[ ] by P t (A/A[ ]), i.e.,

This paper gives the upper and lower bounds on the Perron root of A. An upper bound on Perron root is derived from the maximum of the given parameter t 0 and the maximum of the row sums of P t 0 (A/A[ ]), synchronously, a lower bound on Perron root is expressed by the minimum of the given parameter t 0 and the minimum of the row sums of P t 0 (A/A[ ]). It is also shown how to choose the parameter t after to get tighter upper and lower bounds of (A). Several numerical examples are presented to show that our method compared with the methods in [L.