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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)
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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 · doi:10.1287/opre.21.1.247
[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 · doi:10.1007/BF01588326
[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
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