The distance of potentially stable sign patterns to the unstable matrices

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dc.contributor.authorLin, Qingen_US
dc.date.accessioned2024-08-14T21:05:57Z
dc.date.available2024-08-14T21:05:57Z
dc.date.copyright2001en_US
dc.date.issued2001
dc.degree.departmentDepartment of Computer Science
dc.degree.levelMaster of Science M.Sc.en
dc.description.abstractThe relative distance of a potentially stable sign pattern to the unstable matrices is introduced. The computation of the precise value of this distance is a nonlinear optimization problem. For order 2, an optimal stable matrix in the unique minimally potentially stable sign pattern is determined analyt­ically. This analysis of the order 2 minimally potentially stable sign pattern shows how difficult the computation of this distance can be. Furthermore. it is shown that this distance can be arbitrarily small for potentially stable sign patterns of large order. Therefore, an adequate estimation of this distance becomes increasingly important. A solution is introduced for such an estimation. Firstly, guided by the heuristic hierarchy of the minimally potentially stable tree sign patterns, graph theory is used to obtain a good minimal subpattern. Secondly, a sequence of algorithms is introduced to estimate the distance to the unstable matrices of the minimal components of this subpattern that. have a properly signed nest. The algorithms are applied to those order 3 and 4 minimally po­tentially stable tree sign patterns that have a properly signed nest, as well as to order 5 minimally potentially stable rooted tree sign pat.terns. An ad hoc procedure is used to find a good st.able matrix in each of the two minimally potentially stable tree sign patterns of order 4 that. do not have a properly signed nest.
dc.format.extent100 pages
dc.identifier.urihttps://hdl.handle.net/1828/18683
dc.rightsAvailable to the World Wide Weben_US
dc.titleThe distance of potentially stable sign patterns to the unstable matricesen_US
dc.typeThesisen_US

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