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Joint bounds for the Perron roots of nonnegative matrices with applications.
- Source :
-
Journal of Mathematical Sciences . Mar2007, Vol. 141 Issue 6, p1586-1600. 15p. - Publication Year :
- 2007
-
Abstract
- Given a finite set {Ax}x ∈ X of nonnegative matrices, we derive joint upper and lower bounds for the row sums of the matrices D−1 A(x) D, x ∈ X, where D is a specially chosen nonsingular diagonal matrix. These bounds, depending only on the sparsity patterns of the matrices A(x) and their row sums, are used to obtain joint two-sided bounds for the Perron roots of given nonnegative matrices, joint upper bounds for the spectral radii of given complex matrices, bounds for the joint and lower spectral radii of a matrix set, and conditions sufficient for all convex combinations of given matrices to be Schur stable. Bibliography: 20 titles. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10723374
- Volume :
- 141
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 23961679
- Full Text :
- https://doi.org/10.1007/s10958-007-0067-8