Maximizing the spectral radius of a matrix product

Elsner L, Hadeler KP (2015)
Linear Algebra and its Applications 469: 153-168.

Zeitschriftenaufsatz | Veröffentlicht| Englisch
 
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Autor/in
Elsner, LudwigUniBi; Hadeler, Karl Peter
Abstract / Bemerkung
For a non-negative matrix A the spectral radius of the product XA is maximized over all non-negative diagonal matrices X with trace 1. Instead of following the naive approach of solving a sequence of matrix eigenvalue problems, we construct a related minimization problem, with a rather simple gradient flow, and follow this flow with a steepest descent method. This procedure gives lower bounds and eventually the solution with desired accuracy. On the other hand, we obtain an upper bound in the form of the max algebra Perron root of the matrix A (and some refined upper bounds). Numerical experiments show that in many cases the upper bound is a surprisingly good estimate. (C) 2014 Elsevier Inc. All rights reserved.
Stichworte
Optimal; Steepest descent; Power method; Max algebra; Perron root; allocation; Basic reproduction number
Erscheinungsjahr
2015
Zeitschriftentitel
Linear Algebra and its Applications
Band
469
Seite(n)
153-168
ISSN
0024-3795
Page URI
https://pub.uni-bielefeld.de/record/2723769

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Elsner L, Hadeler KP. Maximizing the spectral radius of a matrix product. Linear Algebra and its Applications. 2015;469:153-168.
Elsner, L., & Hadeler, K. P. (2015). Maximizing the spectral radius of a matrix product. Linear Algebra and its Applications, 469, 153-168. doi:10.1016/j.laa.2014.10.046
Elsner, L., and Hadeler, K. P. (2015). Maximizing the spectral radius of a matrix product. Linear Algebra and its Applications 469, 153-168.
Elsner, L., & Hadeler, K.P., 2015. Maximizing the spectral radius of a matrix product. Linear Algebra and its Applications, 469, p 153-168.
L. Elsner and K.P. Hadeler, “Maximizing the spectral radius of a matrix product”, Linear Algebra and its Applications, vol. 469, 2015, pp. 153-168.
Elsner, L., Hadeler, K.P.: Maximizing the spectral radius of a matrix product. Linear Algebra and its Applications. 469, 153-168 (2015).
Elsner, Ludwig, and Hadeler, Karl Peter. “Maximizing the spectral radius of a matrix product”. Linear Algebra and its Applications 469 (2015): 153-168.