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Some closer bounds of Perron root basing on generalized Perron complement

✍ Scribed by Zhi-Ming Yang

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
322 KB
Volume
235
Category
Article
ISSN
0377-0427

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✦ Synopsis

This paper is concerned with the bounds of the Perron root ρ(A) of a nonnegative irreducible matrix A. Two new methods utilizing the relationship between the Perron root of a nonnegative irreducible matrix and its generalized Perron complements are presented.

The former method is efficient because it gives the bounds for ρ(A) only by calculating the row sums of the generalized Perron complement P t (A/A[α]) or even the row sums of submatrices

And the latter gives the closest bounds (just in this paper) of ρ(A). The results obtained by these methods largely improve the classical bounds. Numerical examples are given to illustrate the procedure and compare it with others, which shows that these methods are effective.

πŸ“œ SIMILAR VOLUMES

The lower and upper bounds on Perron roo
The lower and upper bounds on Perron root of nonnegative irreducible matrices
✍ Guang-Xin Huang; Feng Yin; Ke Guo πŸ“‚ Article πŸ“… 2008 πŸ› Elsevier Science 🌐 English βš– 155 KB

Let A be an n Γ— 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 u