×

zbMATH — the first resource for mathematics

An analytical expression and an algorithm for the volume of a convex polyhedron in \(R^ n\). (English) Zbl 0487.52006

MSC:
52Bxx Polytopes and polyhedra
51M25 Length, area and volume in real or complex geometry
52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Cohen, J., andHickey, T.,Two Algorithms for Determining Volumes of Convex Polyhedra, Journal of ACM, Vol. 26, No. 3, 1979. · Zbl 0403.68067
[2] Merkhofer, M. W.,The Value of Information Given Decision Flexibility, Management Science, Vol. 23, No. 7, 1977. · Zbl 0358.90006
[3] Mattheiss, T. H.,An Algorithm for Determining Irrelevant Constraints and All Vertices in Systems of Linear Inequalities, Operations Research, Vol. 21, pp. 247-260, 1973. · Zbl 0265.90024
[4] Grunbaum, B.,Convex Polytopes, Urley, New York, New York, 1967.
[5] Mattheiss, T. H., andSchmidt, B. K.,Computational Results on an Algorithm for Finding All Vertices of a Polytope, Mathematical Programming, Vol. 18, pp. 308-329, 1980. · Zbl 0433.90045
[6] Berger, M.,Geométrie, Volume 3, Polyèdres Convexes et Polytopes, Polyèdres Réguliers, Aires et Volumes, Nathan, Paris, France, 1978.
[7] Dantzig, G. B.,Linear Programming and Extension, Princeton University Press, Princeton, New Jersey, 1963. · Zbl 0108.33103
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.