Eigenproblem for monotone and toeplitz matrices in a Max-algebra

Author: Ján Plavka

Source: Optimization, Volume 53, Number 1, February 2004 , pp. 95-101(7)

Buy & download fulltext article:

Price: $56.94 plus tax (Refund Policy)

Abstract:

The eigenproblem for monotone and Toeplitz matrices in a max-algebra is shown to be solvable in O(n²) time. Two algorithms are described which, for a given n × n real monotone and for a given n × n real Toeplitz matrix compute an eigenvalue lambda

and all eigenvectors of the form x = (x₁, x₂, … , x_n) such that These results improve standard O(n³) algorithms used in the general case.

Keywords: Eigenproblem; Monotone matrix; Toeplitz matrix; Mathematics Subject Classifications 2000: Primary:; Secondary: 05B35

Document Type: Research article

DOI: http://dx.doi.org/10.1080/02331930410001661497

Affiliations: 1: Department of Mathematics Faculty of Electrical Engineering and Informatics University of Technology B. Ne breve mcovej 32 04200 Ko scaron ice Slovakiamcovej 32 04200 Ko scaron ice Slovakia">