On the power method in max algebra

Elsner L, van den Driessche P (1999)
In: Linear Algebra and its Applications. Linear Algebra and its Applications, 302-303. ELSEVIER SCIENCE INC: 17-32.

Konferenzbeitrag | Veröffentlicht | Englisch
 
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Autor*in
Elsner, LudwigUniBi; van den Driessche, Pauline
Abstract / Bemerkung
The eigenvalue problem for an irreducible nonnegative matrix A = [a(ij)] in the max algebra system is A x x = lambda x, where (A x x)(i) = max(j)(a(ij)x(j)) and lambda turns out to be the maximum circuit geometric mean, mu(A). A power method algorithm is given to compute mu(A) and eigenvector x. The algorithm is developed by using results on the convergence of max powers of A, which are proved using nonnegative matrix theory. In contrast to an algorithm developed in [4], this new method works for any irreducible nonnegative A, and calculates eigenvectors in a simpler and more efficient way. Some asymptotic formulas relating mu(A), the spectral radius and norms are also given. (C) 1999]Elsevier Science Inc. All rights reserved.
Erscheinungsjahr
1999
Titel des Konferenzbandes
Linear Algebra and its Applications
Band
302-303
Seite(n)
17-32
ISSN
0024-3795
Page URI
https://pub.uni-bielefeld.de/record/1620985

Zitieren

Elsner L, van den Driessche P. On the power method in max algebra. In: Linear Algebra and its Applications. Linear Algebra and its Applications. Vol 302-303. ELSEVIER SCIENCE INC; 1999: 17-32.
Elsner, L., & van den Driessche, P. (1999). On the power method in max algebra. Linear Algebra and its Applications, Linear Algebra and its Applications, 302-303, 17-32. ELSEVIER SCIENCE INC. https://doi.org/10.1016/S0024-3795(98)10171-4
Elsner, L., and van den Driessche, P. (1999). “On the power method in max algebra” in Linear Algebra and its Applications Linear Algebra and its Applications, vol. 302-303, (ELSEVIER SCIENCE INC), 17-32.
Elsner, L., & van den Driessche, P., 1999. On the power method in max algebra. In Linear Algebra and its Applications. Linear Algebra and its Applications. no.302-303 ELSEVIER SCIENCE INC, pp. 17-32.
L. Elsner and P. van den Driessche, “On the power method in max algebra”, Linear Algebra and its Applications, Linear Algebra and its Applications, vol. 302-303, ELSEVIER SCIENCE INC, 1999, pp.17-32.
Elsner, L., van den Driessche, P.: On the power method in max algebra. Linear Algebra and its Applications. Linear Algebra and its Applications. 302-303, p. 17-32. ELSEVIER SCIENCE INC (1999).
Elsner, Ludwig, and van den Driessche, Pauline. “On the power method in max algebra”. Linear Algebra and its Applications. ELSEVIER SCIENCE INC, 1999.Vol. 302-303. Linear Algebra and its Applications. 17-32.

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