On the boundedness of an iteration involving points on the hypersphere
نویسندگان
چکیده
For a finite set of points X on the unit hypersphere in R we consider the iteration ui+1 = ui +χi, where χi is the point of X farthest from ui. Restricting to the case where the origin is contained in the convex hull of X we study the maximal length of ui. We give sharp upper bounds for the length of ui independently of X . Precisely, this upper bound is infinity for d ≥ 3 and √ 2 for d = 2.
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ورودعنوان ژورنال:
- Int. J. Comput. Geometry Appl.
دوره 22 شماره
صفحات -
تاریخ انتشار 2012