@techreport{oai:tsukuba.repo.nii.ac.jp:00000347,
author = {後藤, 順哉 and 今野, 浩 and Gotoh, Junya and Konno, Hiroshi},
month = {},
note = {In this paper, we will propose algorithms for calculating a minimal ellipsoid circumscribing a polytope defined by a system of linear inequalities.If we know all vertices of the polytope and its cardinality is not very large,we can solve the problem in an efficient manner by a number of existent algorithms .However,when the polytope is defined by linear inequalities, these algorithms may not work since the cardinality of vertices may be huge.Based on a fact that vertices determining an ellipsoid are only a fraction of these vertices,we propose algorithms which iteratively calculate an ellipsoid which covers a subset of vertices.Numerical experiment shows that these algorithms perform well for polytopes of dimension up to seven.},
title = {Minimal ellipsoid circumscribing a polytope defined by a system of linear inequalities},
year = {2003}
}