The approximate Determinantal Assignment Problem

Leventides, J., Petroulakis, G. & Karcanias, N. (2014). The approximate Determinantal Assignment Problem. Linear Algebra and its Applications, 461, pp. 139-162. doi: 10.1016/j.laa.2014.07.008

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Abstract

The Determinantal Assignment Problem (DAP) has been introduced as the unifying description of all frequency assignment problems in linear systems and it is studied in a projective space setting. This is a multi-linear nature problem and its solution is equivalent to finding real intersections between a linear space, associated with the polynomials to be assigned, and the Grassmann variety of the projective space. This paper introduces a new relaxed version of the problem where the computation of the approximate solution, referred to as the approximate DAP, is reduced to a distance problem between a point in the projective space from the Grassmann variety Gm(Rn). The cases G2(Rn) and its Hodge-dual Gn−2(Rn) are examined and a closed form solution to the distance problem is given based on the skew-symmetric matrix description of multivectors via the gap metric. A new algorithm for the calculation of the approximate solution is given and stability radius results are used to investigate the acceptability of the resulting perturbed solutions.

Item Type: Article
Additional Information: © 2014, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Uncontrolled Keywords: Algebraic methods; Pole and zero placement problems; Exterior Algebra; Approximations
Subjects: Q Science > QA Mathematics
Divisions: School of Engineering & Mathematical Sciences > Engineering
URI: http://openaccess.city.ac.uk/id/eprint/7280

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