Conjugate adaptive algorithms for polyhedral approximation of convex bodies. (Russian, English) Zbl 1099.68757

Kamenev, G. K.

Zh. Vychisl. Mat. Mat. Fiz. 42, No. 9, 1351-1367 (2002); translation in Comput. Math. Math. Phys. 42, No. 9, 1301-1316 (2002).

The duality theory of convex bodies is used to establish the relationship between adaptive algorithms for internal and external polyhedral approximation of convex compact bodies. New algorithms for external approximation of bodies defined by their distance function are proposed and analyzed. The algorithms are conjugate analogs of well-known optimal methods. It is proved that these algorithms are optimal with respect to the order of facets in approximating polyhedra.

Reviewer: Evgenij Nechaev (Moskva)

MSC:

68U05	Computer graphics; computational geometry (digital and algorithmic aspects)
52A27	Approximation by convex sets

Keywords:

conjugate adaptive algorithms; duality theory; convex compact body; distance function