Error Control in Polytope Computations

This paper presents solutions for numerical computation on convex hulls; computational algorithms that ensure logical consistency and accuracy are proposed. A complete numerical error analysis is presented. It is shown that a global error bound for vertex-facet adjacency does not exist under logically consistent procedures. To cope with practical requirements, vertex preconditioned polytope computations are introduced using point and hyperplane adjustments. A global bound on vertex-facet adjacency error is affected by the global bound on vertices; formulas are given for a conservative choice of global error bounds.