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Journal of Mathematical Sciences

, Volume 141, Issue 6, pp 1586–1600 | Cite as

Joint bounds for the Perron roots of nonnegative matrices with applications

  • Yu. A. Al’pin
  • L. Yu. Kolotilina
  • N. N. Korneeva
Article
  • 31 Downloads

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.

Keywords

Spectral Radius Convex Combination Complex Matrice Nonnegative Matrix Sparsity Pattern 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • Yu. A. Al’pin
    • 1
  • L. Yu. Kolotilina
    • 2
  • N. N. Korneeva
    • 1
  1. 1.Kazan’ State UniversityKazan’Russia
  2. 2.St.Petersburg Department of the Steklov Mathematical InstituteSt.PetersburgRussia

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