On the boundedness of an iteration involving points on the hypersphere

Details On the boundedness of an iteration involving points on the hypersphere On the boundedness of an iteration involving points on the hypersphere

2010-01-11

arxiv.org/abs/1001.1624v2

Computer Science

Computational Geometry

Scientific paper

For a finite set of points $X$ on the unit hypersphere in $\mathbb{R}^d$ we consider the iteration $u_{i+1}=u_i+\chi_i$, where $\chi_i$ is the point of $X$ farthest from $u_i$. Restricting to the case where the origin is contained in the convex hull of $X$ we study the maximal length of $u_i$. We give sharp upper bounds for the length of $u_i$ independently of $X$. Precisely, this upper bound is infinity for $d\ge 3$ and $\sqrt2$ for $d=2$.

Affiliated with

Also associated with

No associations

Rating

On the boundedness of an iteration involving points on the hypersphere does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the boundedness of an iteration involving points on the hypersphere, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the boundedness of an iteration involving points on the hypersphere will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-719056