Modifying the power method in max algebra

Elsner L, van den Driessche P (2001)
Linear Algebra and its Applications 332-334: 3-13.

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Konferenzbeitrag | Veröffentlicht | Englisch
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Abstract / Bemerkung
In the max algebra system, the eigenequation for an n x n irreducible nonnegative matrix A = [a(ij)] is A circle times x = mu (A)x. Here (A circle times x)(i) = max(j) a(ij)x(j) and mu (A) is the maximum circuit geometric mean. The complexity of the power method given in [L. Elsner, P. van den Driessche, Linear Algebra Appl., to appear] to compute mu (A) and x is considered. Under some assumptions on the critical matrix, it is shown that the algorithm may have time complexity O(n(4)), A modified power method, based on Karp's formula, is presented. For this new algorithm, with no assumptions on the critical matrix, mu (A) and x can be computed in O(n(3)) time. Furthermore, this algorithm can be used to compute all linearly independent eigenvectors corresponding to mu (A). (C) 2001 Elsevier Science Inc. All rights reserved.
Erscheinungsjahr
Band
332-334
Seite(n)
3-13
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Elsner L, van den Driessche P. Modifying the power method in max algebra. Linear Algebra and its Applications. 2001;332-334:3-13.
Elsner, L., & van den Driessche, P. (2001). Modifying the power method in max algebra. Linear Algebra and its Applications, 332-334, 3-13. doi:10.1016/S0024-3795(00)00062-8
Elsner, L., and van den Driessche, P. (2001). Modifying the power method in max algebra. Linear Algebra and its Applications 332-334, 3-13.
Elsner, L., & van den Driessche, P., 2001. Modifying the power method in max algebra. Linear Algebra and its Applications, 332-334, p 3-13.
L. Elsner and P. van den Driessche, “Modifying the power method in max algebra”, Linear Algebra and its Applications, vol. 332-334, 2001, pp. 3-13.
Elsner, L., van den Driessche, P.: Modifying the power method in max algebra. Linear Algebra and its Applications. 332-334, 3-13 (2001).
Elsner, Ludwig, and van den Driessche, Pauline. “Modifying the power method in max algebra”. Linear Algebra and its Applications 332-334 (2001): 3-13.