Geodesic
Polyhedral approximation of convex compact bodies by filling methods
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 5, pp. 818-828 Cet article a éte moissonné depuis la source Math-Net.Ru

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A class of iterative methods – filling methods – for polyhedral approximation of convex compact bodies is introduced and studied. In contrast to augmentation methods, the vertices of the approximating polytope can lie not only on the boundary of the body but also inside it. Within the proposed class, Hausdorff or $H$-methods of filling are singled out, for which the convergence rates (asymptotic and at the initial stage of the approximation) are estimated. For the approximation of nonsmooth convex compact bodies, the resulting convergence rate estimates coincide with those for augmentation $H$-methods. 
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G. K. Kamenev; A. I. Pospelov. Polyhedral approximation of convex compact bodies by filling methods. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 5, pp. 818-828. http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_5_a5/

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