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The experimental analysis of a new adaptive method for a polyhedral approximation of multidimensional convex bodies. (Russian, English) Zbl 1075.52504

Zh. Vychisl. Mat. Mat. Fiz. 43, No. 3, 328-346 (2003); translation in Comput. Math. Math. Phys. 43, No. 3, 314-330 (2003).
The results of an experimental study of a new adaptive method for approximating convex compact bodies by polytopes (modified method of mutually converging polytopes) are presented. The technique, software, and results of a computer experiment on the approximation of multidimensional ellipsoids are described. Experimental data are used to analyze the constants characterizing the convergence of the method and to compare them with the constants corresponding to the best approximating polytopes.

MSC:

52A27 Approximation by convex sets
65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
41A25 Rate of convergence, degree of approximation
41A63 Multidimensional problems
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