Max-algebra and pairwise comparison matrices, II

Elsner L, van den Driessche P (2010)
Linear Algebra and its Applications 432(4): 927-935.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Elsner, LudwigUniBi; van den Driessche, Pauline
Abstract / Bemerkung
This paper is a continuation of our 2004 paper "Max-algebra and pairwise comparison matrices", in which the max-eigenvector of a symmetrically reciprocal matrix was used to approximate such a matrix by a transitive matrix. This approximation was based on minimizing the maximal relative error. In a later paper by Dahl a different error measure was used and led to a slightly different approximating transitive matrix. Here some geometric properties of this approximation problem are discussed. These lead, among other results, to a new characterization of a max-eigenvector of an irreducible nonnegative matrix. The case of Toeplitz matrices is discussed in detail, and an application to music theory that uses Toeplitz symmetrically reciprocal matrices is given. (C) 2009 Elsevier Inc. All rights reserved.
Stichworte
Perturbations; Toeplitz matrix; Music theory; Max-eigenvector; SR-matrix
Erscheinungsjahr
2010
Zeitschriftentitel
Linear Algebra and its Applications
Band
432
Ausgabe
4
Seite(n)
927-935
ISSN
0024-3795
Page URI
https://pub.uni-bielefeld.de/record/1588828

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Elsner L, van den Driessche P. Max-algebra and pairwise comparison matrices, II. Linear Algebra and its Applications. 2010;432(4):927-935.
Elsner, L., & van den Driessche, P. (2010). Max-algebra and pairwise comparison matrices, II. Linear Algebra and its Applications, 432(4), 927-935. doi:10.1016/j.laa.2009.10.005
Elsner, L., and van den Driessche, P. (2010). Max-algebra and pairwise comparison matrices, II. Linear Algebra and its Applications 432, 927-935.
Elsner, L., & van den Driessche, P., 2010. Max-algebra and pairwise comparison matrices, II. Linear Algebra and its Applications, 432(4), p 927-935.
L. Elsner and P. van den Driessche, “Max-algebra and pairwise comparison matrices, II”, Linear Algebra and its Applications, vol. 432, 2010, pp. 927-935.
Elsner, L., van den Driessche, P.: Max-algebra and pairwise comparison matrices, II. Linear Algebra and its Applications. 432, 927-935 (2010).
Elsner, Ludwig, and van den Driessche, Pauline. “Max-algebra and pairwise comparison matrices, II”. Linear Algebra and its Applications 432.4 (2010): 927-935.