Abstract
We propose and analyze the stepwisesupplement� ofacovering (SWSC) method intended for con� structing a suboptimal sequence of coverings of the multidimensional unit sphere by neighborhoods of a finite number of points. The construction of such cov� erings is of great practical importance. Specifically, they can be used in the polyhedral approximation of multidimensional convex compact bodies (CCBs) based on the evaluation of their support function for directions defined by points generating a covering, for example, in the approximation of reachable sets of dynamical systems (1) and sets of reachable criteria vectors in multicriteria optimization problems (2, 3). Methods for constructing optimal coverings are available only in the twodimensional case. As a result, coverings that are far from being optimal are used in practice (e.g., coverings obtained by using multidi� mensional polar coordinates). In this paper, we describe the SWSC method and present results of a theoretical and experimental analysis of coverings produced by this method. More specifically, asymp� totic estimates for the ratio of the radii of an optimal covering and one constructed by the SWSC method are given and the radii of the SWSCbased coverings are compared with that of the coverings based on polar coordinates.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
