Iterative refinement for invariant subspaces of matrices with application to the Promethee-Gaia method
(2008) International Journal of Pure and Applied Mathematics — Vol. 47, n° 4, p. 501-518 (2008)
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- Authors
Meskens, Nadine 
- Abstract
- Recent results in Operational Research have provided decision makers with a highly adaptable tool that is able to quickly synthesize the performance measures of several solutions to be compared in a lim- ited time. In the context of multicriteria limited-time decision making problems, two of the authors have developed hybrid models composed of two mathematical models, a set of dedicated heuristics, a stochastic local search, meta-heuristic and a simulation model. According to the decision makers, the solutions are ranked on the basis of several criteria whose importance determines this ranking. A multicriteria method is incoporated into the hybrid. In order to summarize the huge amount of resulting data/information, we have embeded the Promethee II multicriteria method and the GAIA plane. This extension requires to compute eigenelements on the output produced by Promethee. Eigenelement computation is proposed here in two steps: 1) Get some rough approximation to the desired part of the spectrum and the cor- responding maximal invariant subspace, and 2) Refine this approximation with an iterative scheme. A Newton-based scheme is proposed in this paper and applied to a matrix issued from the Promethee-Gaia method.
- Affiliations
Louvain School of Management Operations and Information
Citations
Ahues, M., Duvivier, D., Largillier, A., & Meskens, N. (2008). Iterative refinement for invariant subspaces of matrices with application to the Promethee-Gaia method. International Journal of Pure and Applied Mathematics, 47(4), 501-518. https://hdl.handle.net/2078.5/249887 (Original work published 2008)